Intro_to_PP_edward.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAV0AAABECAYAAAAiJuZQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nPQpWNmHZBnMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24aef6843c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import edward as ed\n",
    "from edward.models import Uniform\n",
    "from edward.models import Bernoulli\n",
    "import tensorflow as tf\n",
    "\n",
    "from __future__ import absolute_import\n",
    "from __future__ import division\n",
    "from __future__ import print_function\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.cm as cm\n",
    "from matplotlib.colors import ListedColormap, Normalize\n",
    "from matplotlib.animation import FuncAnimation\n",
    "from tempfile import NamedTemporaryFile\n",
    "from IPython.display import HTML\n",
    "\n",
    "import seaborn as sns\n",
    "import numpy as np\n",
    "import six\n",
    "import matplotlib\n",
    "matplotlib.interactive(True)\n",
    "\n",
    "plt.style.use('seaborn-talk')\n",
    "sns.set_context(\"talk\", font_scale=1.4)\n",
    "sess = ed.get_session()\n",
    "\n",
    "sns.palplot(sns.color_palette())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# initialize a random seed for edward. Can be done ONCE only before using Edward\n",
    "ed.set_seed(42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "VIDEO_TAG = \"\"\"<video controls> \n",
    " <source src=\"data:video/x-m4v;base64,{0}\" type=\"video/mp4\">\n",
    " Your browser does noet support the video tag\n",
    "</video>\"\"\"\n",
    "\n",
    "def anim_to_html(anim):\n",
    "    if not hasattr(anim, '_encoded_video'):\n",
    "        with NamedTemporaryFile(suffix='.mp4') as f:\n",
    "            anim.save(f.name, fps=20, extra_args=['-vcodec', 'libx264'])\n",
    "            video = open(f.name, \"rb\").read()\n",
    "        anim._encoded_video = video.encode(\"base64\")\n",
    "        \n",
    "    return VIDEO_TAG.format(anim._encoded_video)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Coin"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from edward.models import Bernoulli, Beta, Empirical, Uniform"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "N = 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def build_fair_dataset(N):\n",
    "    pheads = tf.constant(0.5)\n",
    "    c = Bernoulli(probs=pheads, sample_shape = N)\n",
    "    return sess.run([pheads, c])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def build_unfair_dataset(N):\n",
    "    pheads = tf.constant(0.05)\n",
    "    c = Bernoulli(probs=pheads, sample_shape = N)\n",
    "    return sess.run([pheads, c])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def build_dataset(N):\n",
    "    pheads = Uniform(low=0.0,high=1.0)\n",
    "    c = Bernoulli(probs=pheads, sample_shape = N)\n",
    "    return sess.run([pheads, c])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x24a8b68f240>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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nq7y83BPdBAAAMJ0gd79hQUGBxo4dq8LCQo0bN07BwcFasWKFRo0apU2bNik8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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24af58dc518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = tf.range(-0.2, 1.2, 0.001)\n",
    "\n",
    "plt.plot(*sess.run([x, Uniform(low=0.0,high=1.0).prob(x)]));\n",
    "plt.ylim((-0.2,1.2))\n",
    "plt.title('Uniform distribution')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pheads_true,c_train = build_fair_dataset(N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pheads_true"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0,\n       1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1,\n       1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1,\n       0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1,\n       1, 1, 1, 0, 0, 1, 0, 1])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c_train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "50"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(c_train == 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "50"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(c_train == 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## inference"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# declaring priors\n",
    "\n",
    "pheads_fair = Beta(concentration1=1000.0, concentration0=1000.0) # blue\n",
    "pheads_unfair = Beta(concentration1=0.1, concentration0=0.1) # green\n",
    "\n",
    "pheads_unknown = Beta(concentration1 = 1.0, concentration0=1.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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9ipdffjl1X3NzM1544QXMmTMnK/A5j4fZE4ksFk9X4PJlhj1uI0IkJjcVfXod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\nRJRmGOCIiIiI0sw/fSqyue1V4OMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24a90d38e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = tf.range(0.0,1.0,0.001)\n",
    "plt.plot(*sess.run([x, pheads_fair.prob(x)]));\n",
    "plt.plot(*sess.run([x, pheads_unfair.prob(x)]));\n",
    "plt.plot(*sess.run([x, pheads_unknown.prob(x)]));\n",
    "plt.axvline(x=pheads_true);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Forward model\n",
    "pheads = pheads_unknown\n",
    "c = Bernoulli(probs=pheads, sample_shape=N)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### exact solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# inference\n",
    "pheads_cond = ed.complete_conditional(pheads)\n",
    "pheads_post = ed.copy(pheads_cond, {c: c_train})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'concentration0': 51.0, 'concentration1': 51.0}"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sess.run({key:val for key, val in six.iteritems(pheads_post.parameters) if isinstance(val,tf.Tensor)})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " exact posterior mean: 0.5\nexact posterior std0.0492665\n"
     ]
    }
   ],
   "source": [
    "# criticism\n",
    "mean, stddev = sess.run([pheads_post.mean(),pheads_post.stddev()])\n",
    "print(\" exact posterior mean: \" + str(mean))\n",
    "print(\"exact posterior std\" + str(stddev))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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jDm3atEm33nqrEomEmzUBKFCRxKCiySFJUqiI9pg5IbQ/NqBYMq7SQNDjigD4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\ngCau/byJQImAbJ0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24a974abe48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = tf.range(0.0,1.0,0.001)\n",
    "plt.plot(*sess.run([x,pheads.prob(x)]));\n",
    "plt.plot(*sess.run([x,pheads_post.prob(x)]));\n",
    "plt.axvline(x=pheads_true);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## RECURSIVE INFERENCE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "finished recursion 1\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "finished recursion 2\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "finished recursion 3\n"
     ]
    },
    {
     "data": {
      "image/png": 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GP7OorR5Otw1QgQahlioTkdlYgRPMxClUZnBEpWLPNm0adP6SuuzU6HSsVgva1jQDAPwQ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\niAQjAZwQQgghRIKRAE4IIYQQIsH8fw1x+M64au2tAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24a8fc18630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pheads_true,c_train = build_fair_dataset(100)\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = plt.axes(xlim=(-0.05,1.05), ylim=(-1.0,11.0))\n",
    "\n",
    "def go(pheads_prior, sample_shape, c_train, recursion=1):\n",
    "    # model \n",
    "    c = Bernoulli(probs=pheads_prior,\n",
    "                 sample_shape=sample_shape)\n",
    "    \n",
    "    # INFERENCE\n",
    "    pheads_cond = ed.complete_conditional(pheads_prior)\n",
    "    pheads_post = ed.copy(pheads_cond,{c:c_train[:sample_shape]})\n",
    "    \n",
    "    # CRITICISM\n",
    "    ax.plot(*sess.run([x,pheads_post.prob(x)]));\n",
    "    \n",
    "    print(\"finished recursion \"+str(recursion))\n",
    "    recursion += 1\n",
    "    # RECURSION\n",
    "    if len(c_train[sample_shape:]) >= sample_shape:\n",
    "        go(pheads_post, sample_shape, c_train[sample_shape:],recursion)\n",
    "        \n",
    "pheads_prior = Beta(concentration1=0.1, concentration0=0.1)\n",
    "ax.plot(*sess.run([x, pheads_prior.prob(x)])); \n",
    "plt.axvline(x=pheads_true);\n",
    "go(pheads_prior,33,c_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## approximate inference :MCMC: metroplis hastings:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# BACKWARD MODEL\n",
    "T = 10000\n",
    "q_pheads = Empirical(params=tf.Variable(tf.ones([T])*0.5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\r    1/10000 [  0%]                                ETA: 9777s | Acceptance Rate: nan"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r  100/10000 [  1%]                                ETA: 121s | Acceptance Rate: 0.182"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r  200/10000 [  2%]                                ETA: 71s | Acceptance Rate: 0.151 "
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r  300/10000 [  3%]                                ETA: 53s | Acceptance Rate: 0.167"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r  400/10000 [  4%] █                              ETA: 44s | Acceptance Rate: 0.165"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r  500/10000 [  5%] █                              ETA: 38s | Acceptance Rate: 0.170"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r  600/10000 [  6%] █                              ETA: 34s | Acceptance Rate: 0.169"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r  700/10000 [  7%] ██                             ETA: 31s | Acceptance Rate: 0.169"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r  800/10000 [  8%] ██                             ETA: 28s | Acceptance Rate: 0.178"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r  900/10000 [  9%] ██                             ETA: 27s | Acceptance Rate: 0.179"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 1000/10000 [ 10%] ███                            ETA: 25s | Acceptance Rate: 0.171"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 1100/10000 [ 11%] ███                            ETA: 24s | Acceptance Rate: 0.170"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 1200/10000 [ 12%] ███                            ETA: 23s | Acceptance Rate: 0.171"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 1300/10000 [ 13%] ███                            ETA: 22s | Acceptance Rate: 0.170"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 1400/10000 [ 14%] ████                           ETA: 21s | Acceptance Rate: 0.165"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 1500/10000 [ 15%] ████                           ETA: 20s | Acceptance Rate: 0.165"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 1600/10000 [ 16%] ████                           ETA: 20s | Acceptance Rate: 0.166"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 1700/10000 [ 17%] █████                          ETA: 19s | Acceptance Rate: 0.164"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 1800/10000 [ 18%] █████                          ETA: 18s | Acceptance Rate: 0.167"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 1900/10000 [ 19%] █████                          ETA: 18s | Acceptance Rate: 0.166"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 2000/10000 [ 20%] ██████                         ETA: 17s | Acceptance Rate: 0.166"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 2100/10000 [ 21%] ██████                         ETA: 17s | Acceptance Rate: 0.164"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 2200/10000 [ 22%] ██████                         ETA: 17s | Acceptance Rate: 0.165"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 2300/10000 [ 23%] ██████                         ETA: 16s | Acceptance Rate: 0.164"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 2400/10000 [ 24%] ███████                        ETA: 16s | Acceptance Rate: 0.161"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 2500/10000 [ 25%] ███████                        ETA: 15s | Acceptance Rate: 0.159"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 2600/10000 [ 26%] ███████                        ETA: 15s | Acceptance Rate: 0.160"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 2700/10000 [ 27%] ████████                       ETA: 15s | Acceptance Rate: 0.160"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 2800/10000 [ 28%] ████████                       ETA: 14s | Acceptance Rate: 0.159"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 2900/10000 [ 28%] ████████                       ETA: 14s | Acceptance Rate: 0.160"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 3000/10000 [ 30%] █████████                      ETA: 14s | Acceptance Rate: 0.161"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 3100/10000 [ 31%] █████████                      ETA: 13s | Acceptance Rate: 0.161"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 3200/10000 [ 32%] █████████                      ETA: 13s | Acceptance Rate: 0.163"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 3300/10000 [ 33%] █████████                      ETA: 13s | Acceptance Rate: 0.164"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 3400/10000 [ 34%] ██████████                     ETA: 13s | Acceptance Rate: 0.162"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 3500/10000 [ 35%] ██████████                     ETA: 12s | Acceptance Rate: 0.164"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 3600/10000 [ 36%] ██████████                     ETA: 12s | Acceptance Rate: 0.163"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 3700/10000 [ 37%] ███████████                    ETA: 12s | Acceptance Rate: 0.162"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 3800/10000 [ 38%] ███████████                    ETA: 12s | Acceptance Rate: 0.162"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 3900/10000 [ 39%] ███████████                    ETA: 11s | Acceptance Rate: 0.160"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 4000/10000 [ 40%] ████████████                   ETA: 11s | Acceptance Rate: 0.161"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 4100/10000 [ 41%] ████████████                   ETA: 11s | Acceptance Rate: 0.161"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 4200/10000 [ 42%] ████████████                   ETA: 11s | Acceptance Rate: 0.161"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 4300/10000 [ 43%] ████████████                   ETA: 10s | Acceptance Rate: 0.161"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 4400/10000 [ 44%] █████████████                  ETA: 10s | Acceptance Rate: 0.160"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 4500/10000 [ 45%] █████████████                  ETA: 10s | Acceptance Rate: 0.159"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 4600/10000 [ 46%] █████████████                  ETA: 10s | Acceptance Rate: 0.159"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 4700/10000 [ 47%] ██████████████                 ETA: 10s | Acceptance Rate: 0.158"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 4800/10000 [ 48%] ██████████████                 ETA: 9s | Acceptance Rate: 0.158 "
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 4900/10000 [ 49%] ██████████████                 ETA: 9s | Acceptance Rate: 0.158"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 5000/10000 [ 50%] ███████████████                ETA: 9s | Acceptance Rate: 0.157"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 5100/10000 [ 51%] ███████████████                ETA: 9s | Acceptance Rate: 0.157"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 5200/10000 [ 52%] ███████████████                ETA: 8s | Acceptance Rate: 0.158"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 5300/10000 [ 53%] ███████████████                ETA: 8s | Acceptance Rate: 0.157"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 5400/10000 [ 54%] ████████████████               ETA: 8s | Acceptance Rate: 0.158"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 5500/10000 [ 55%] ████████████████               ETA: 8s | Acceptance Rate: 0.159"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 5600/10000 [ 56%] ████████████████               ETA: 8s | Acceptance Rate: 0.158"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 5700/10000 [ 56%] █████████████████              ETA: 7s | Acceptance Rate: 0.158"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 5800/10000 [ 57%] █████████████████              ETA: 7s | Acceptance Rate: 0.159"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 5900/10000 [ 59%] █████████████████              ETA: 7s | Acceptance Rate: 0.159"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 6000/10000 [ 60%] ██████████████████             ETA: 7s | Acceptance Rate: 0.160"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 6100/10000 [ 61%] ██████████████████             ETA: 7s | Acceptance Rate: 0.159"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 6200/10000 [ 62%] ██████████████████             ETA: 6s | Acceptance Rate: 0.161"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 6300/10000 [ 63%] ██████████████████             ETA: 6s | Acceptance Rate: 0.161"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 6400/10000 [ 64%] ███████████████████            ETA: 6s | Acceptance Rate: 0.162"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 6500/10000 [ 65%] ███████████████████            ETA: 6s | Acceptance Rate: 0.161"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 6600/10000 [ 66%] ███████████████████            ETA: 6s | Acceptance Rate: 0.161"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 6700/10000 [ 67%] ████████████████████           ETA: 5s | Acceptance Rate: 0.162"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 6800/10000 [ 68%] ████████████████████           ETA: 5s | Acceptance Rate: 0.161"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 6900/10000 [ 69%] ████████████████████           ETA: 5s | Acceptance Rate: 0.161"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 7000/10000 [ 70%] █████████████████████          ETA: 5s | Acceptance Rate: 0.161"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 7100/10000 [ 71%] █████████████████████          ETA: 5s | Acceptance Rate: 0.162"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 7200/10000 [ 72%] █████████████████████          ETA: 5s | Acceptance Rate: 0.161"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 7300/10000 [ 73%] █████████████████████          ETA: 4s | Acceptance Rate: 0.160"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 7400/10000 [ 74%] ██████████████████████         ETA: 4s | Acceptance Rate: 0.161"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 7500/10000 [ 75%] ██████████████████████         ETA: 4s | Acceptance Rate: 0.161"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 7600/10000 [ 76%] ██████████████████████         ETA: 4s | Acceptance Rate: 0.161"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 7700/10000 [ 77%] ███████████████████████        ETA: 4s | Acceptance Rate: 0.162"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 7800/10000 [ 78%] ███████████████████████        ETA: 3s | Acceptance Rate: 0.162"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 7900/10000 [ 79%] ███████████████████████        ETA: 3s | Acceptance Rate: 0.162"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 8000/10000 [ 80%] ████████████████████████       ETA: 3s | Acceptance Rate: 0.162"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 8100/10000 [ 81%] ████████████████████████       ETA: 3s | Acceptance Rate: 0.162"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 8200/10000 [ 82%] ████████████████████████       ETA: 3s | Acceptance Rate: 0.161"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 8300/10000 [ 83%] ████████████████████████       ETA: 3s | Acceptance Rate: 0.162"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 8400/10000 [ 84%] █████████████████████████      ETA: 2s | Acceptance Rate: 0.163"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 8500/10000 [ 85%] █████████████████████████      ETA: 2s | Acceptance Rate: 0.162"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 8600/10000 [ 86%] █████████████████████████      ETA: 2s | Acceptance Rate: 0.162"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 8700/10000 [ 87%] ██████████████████████████     ETA: 2s | Acceptance Rate: 0.163"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 8800/10000 [ 88%] ██████████████████████████     ETA: 2s | Acceptance Rate: 0.163"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 8900/10000 [ 89%] ██████████████████████████     ETA: 1s | Acceptance Rate: 0.163"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 9000/10000 [ 90%] ███████████████████████████    ETA: 1s | Acceptance Rate: 0.163"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 9100/10000 [ 91%] ███████████████████████████    ETA: 1s | Acceptance Rate: 0.162"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 9200/10000 [ 92%] ███████████████████████████    ETA: 1s | Acceptance Rate: 0.162"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 9300/10000 [ 93%] ███████████████████████████    ETA: 1s | Acceptance Rate: 0.162"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 9400/10000 [ 94%] ████████████████████████████   ETA: 1s | Acceptance Rate: 0.162"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 9500/10000 [ 95%] ████████████████████████████   ETA: 0s | Acceptance Rate: 0.162"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 9600/10000 [ 96%] ████████████████████████████   ETA: 0s | Acceptance Rate: 0.162"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 9700/10000 [ 97%] █████████████████████████████  ETA: 0s | Acceptance Rate: 0.162"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 9800/10000 [ 98%] █████████████████████████████  ETA: 0s | Acceptance Rate: 0.162"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 9900/10000 [ 99%] █████████████████████████████  ETA: 0s | Acceptance Rate: 0.162"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r10000/10000 [100%] ██████████████████████████████ Elapsed: 17s | Acceptance Rate: 0.161"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "# INFERENCE\n",
    "proposal_pheads = Beta(concentration1=1.0,\n",
    "                       concentration0=1.0)\n",
    "inference = ed.MetropolisHastings(latent_vars = {pheads: q_pheads},\n",
    "                                 proposal_vars={pheads: proposal_pheads},\n",
    "                                 data={c:c_train})\n",
    "inference.run()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "inferred posterior mean:\n0.488378\ninferred posterior std:\n0.049427\n"
     ]
    }
   ],
   "source": [
    "# criticism\n",
    "mean, stddev = sess.run([q_pheads.mean(),q_pheads.stddev()])\n",
    "print(\"inferred posterior mean:\")\n",
    "print(mean)\n",
    "print(\"inferred posterior std:\")\n",
    "print(stddev)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x24a975372e8>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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cORoX2Rwi4Z2vF58dqRUPFMWwDWBLmZytPPmoebmYXapoHoOqjp2EVEzBmSas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\nP4IgCIIgiAji/wOtBYU3onlpaAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24a97537320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(q_pheads.params.eval());\n",
    "plt.axhline(y=pheads_true)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def lags(x):\n",
    "    mean = tf.reduce_mean(x)\n",
    "    var = tf.cast(tf.size(x) - 1, tf.float32) *tf.reduce_mean(tf.square(x-mean))\n",
    "    ret = tf.map_fn(lambda k:tf.cond(tf.equal(k,0),\n",
    "                                     lambda:var, \n",
    "                                     lambda:tf.reduce_sum((x[:-k] - mean) * (x[k:]-mean))),\n",
    "                                     tf.range(0,tf.size(x)),\n",
    "                                     dtype=tf.float32)\n",
    "    return ret / var"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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psssuk9Pp1D//+U/NmDFDffv2DehAExNjmjyG1uB6+OjoCCUkxLbpc+HkxcfHnO5DgB+0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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24a9da26ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(lags(q_pheads.params).eval());"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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QLikbe+ASr7d1oF2dXf3yelL3ocd7yR1oJ+dLdxsd6MudZQHupZdeUiQS0YUX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\nDgAAwGUIcAAAAC7z/wNohkrW0ZPdmwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24a9d093cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = tf.range(0.0,1.0,0.001)\n",
    "plt.plot(*sess.run([x,pheads.prob(x)]));\n",
    "plt.plot(*sess.run([x,pheads_cond.prob(x)],\n",
    "                  {c:c_train}));\n",
    "plt.hist(q_pheads.params.eval(),\n",
    "        bins=100,range=(0.0,1.0),\n",
    "        normed = True);\n",
    "plt.axvline(x=pheads_true);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## MCMC: Gibbs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# BACKWARD MODEL\n",
    "T = 10000\n",
    "q_pheads = Empirical(params=tf.Variable(tf.ones([T])*0.5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\r    1/10000 [  0%]                                ETA: 8471s | Acceptance Rate: inf"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r  100/10000 [  1%]                                ETA: 139s | Acceptance Rate: 1.010"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r  200/10000 [  2%]                                ETA: 96s | Acceptance Rate: 1.005 "
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r  300/10000 [  3%]                                ETA: 80s | Acceptance Rate: 1.003"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r  400/10000 [  4%] █                              ETA: 74s | Acceptance Rate: 1.003"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r  500/10000 [  5%] █                              ETA: 71s | Acceptance Rate: 1.002"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r  600/10000 [  6%] █                              ETA: 67s | Acceptance Rate: 1.002"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r  700/10000 [  7%] ██                             ETA: 64s | Acceptance Rate: 1.001"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r  800/10000 [  8%] ██                             ETA: 62s | Acceptance Rate: 1.001"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r  900/10000 [  9%] ██                             ETA: 60s | Acceptance Rate: 1.001"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 1000/10000 [ 10%] ███                            ETA: 56s | Acceptance Rate: 1.001"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 1100/10000 [ 11%] ███                            ETA: 54s | Acceptance Rate: 1.001"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 1200/10000 [ 12%] ███                            ETA: 51s | Acceptance Rate: 1.001"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 1300/10000 [ 13%] ███                            ETA: 49s | Acceptance Rate: 1.001"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 1400/10000 [ 14%] ████                           ETA: 47s | Acceptance Rate: 1.001"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 1500/10000 [ 15%] ████                           ETA: 46s | Acceptance Rate: 1.001"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 1600/10000 [ 16%] ████                           ETA: 45s | Acceptance Rate: 1.001"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 1700/10000 [ 17%] █████                          ETA: 43s | Acceptance Rate: 1.001"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 1800/10000 [ 18%] █████                          ETA: 42s | Acceptance Rate: 1.001"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 1900/10000 [ 19%] █████                          ETA: 41s | Acceptance Rate: 1.001"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 2000/10000 [ 20%] ██████                         ETA: 40s | Acceptance Rate: 1.001"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 2100/10000 [ 21%] ██████                         ETA: 39s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 2200/10000 [ 22%] ██████                         ETA: 38s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 2300/10000 [ 23%] ██████                         ETA: 37s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 2400/10000 [ 24%] ███████                        ETA: 36s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 2500/10000 [ 25%] ███████                        ETA: 35s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 2600/10000 [ 26%] ███████                        ETA: 34s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 2700/10000 [ 27%] ████████                       ETA: 33s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 2800/10000 [ 28%] ████████                       ETA: 32s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 2900/10000 [ 28%] ████████                       ETA: 32s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 3000/10000 [ 30%] █████████                      ETA: 31s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 3100/10000 [ 31%] █████████                      ETA: 30s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 3200/10000 [ 32%] █████████                      ETA: 30s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 3300/10000 [ 33%] █████████                      ETA: 29s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 3400/10000 [ 34%] ██████████                     ETA: 28s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 3500/10000 [ 35%] ██████████                     ETA: 28s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 3600/10000 [ 36%] ██████████                     ETA: 27s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 3700/10000 [ 37%] ███████████                    ETA: 27s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 3800/10000 [ 38%] ███████████                    ETA: 26s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 3900/10000 [ 39%] ███████████                    ETA: 25s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 4000/10000 [ 40%] ████████████                   ETA: 25s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 4100/10000 [ 41%] ████████████                   ETA: 24s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 4200/10000 [ 42%] ████████████                   ETA: 24s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 4300/10000 [ 43%] ████████████                   ETA: 24s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 4400/10000 [ 44%] █████████████                  ETA: 23s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 4500/10000 [ 45%] █████████████                  ETA: 23s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 4600/10000 [ 46%] █████████████                  ETA: 23s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 4700/10000 [ 47%] ██████████████                 ETA: 22s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 4800/10000 [ 48%] ██████████████                 ETA: 22s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 4900/10000 [ 49%] ██████████████                 ETA: 21s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 5000/10000 [ 50%] ███████████████                ETA: 21s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 5100/10000 [ 51%] ███████████████                ETA: 20s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 5200/10000 [ 52%] ███████████████                ETA: 20s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 5300/10000 [ 53%] ███████████████                ETA: 19s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 5400/10000 [ 54%] ████████████████               ETA: 19s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 5500/10000 [ 55%] ████████████████               ETA: 18s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 5600/10000 [ 56%] ████████████████               ETA: 18s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 5700/10000 [ 56%] █████████████████              ETA: 17s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 5800/10000 [ 57%] █████████████████              ETA: 17s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 5900/10000 [ 59%] █████████████████              ETA: 16s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 6000/10000 [ 60%] ██████████████████             ETA: 16s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 6100/10000 [ 61%] ██████████████████             ETA: 16s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 6200/10000 [ 62%] ██████████████████             ETA: 15s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 6300/10000 [ 63%] ██████████████████             ETA: 15s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 6400/10000 [ 64%] ███████████████████            ETA: 14s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 6500/10000 [ 65%] ███████████████████            ETA: 14s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 6600/10000 [ 66%] ███████████████████            ETA: 13s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 6700/10000 [ 67%] ████████████████████           ETA: 13s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 6800/10000 [ 68%] ████████████████████           ETA: 12s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 6900/10000 [ 69%] ████████████████████           ETA: 12s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 7000/10000 [ 70%] █████████████████████          ETA: 12s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 7100/10000 [ 71%] █████████████████████          ETA: 11s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 7200/10000 [ 72%] █████████████████████          ETA: 11s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 7300/10000 [ 73%] █████████████████████          ETA: 10s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 7400/10000 [ 74%] ██████████████████████         ETA: 10s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 7500/10000 [ 75%] ██████████████████████         ETA: 10s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 7600/10000 [ 76%] ██████████████████████         ETA: 9s | Acceptance Rate: 1.000 "
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 7700/10000 [ 77%] ███████████████████████        ETA: 9s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 7800/10000 [ 78%] ███████████████████████        ETA: 8s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 7900/10000 [ 79%] ███████████████████████        ETA: 8s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 8000/10000 [ 80%] ████████████████████████       ETA: 7s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 8100/10000 [ 81%] ████████████████████████       ETA: 7s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 8200/10000 [ 82%] ████████████████████████       ETA: 7s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 8300/10000 [ 83%] ████████████████████████       ETA: 6s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 8400/10000 [ 84%] █████████████████████████      ETA: 6s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 8500/10000 [ 85%] █████████████████████████      ETA: 5s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 8600/10000 [ 86%] █████████████████████████      ETA: 5s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 8700/10000 [ 87%] ██████████████████████████     ETA: 5s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 8800/10000 [ 88%] ██████████████████████████     ETA: 4s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 8900/10000 [ 89%] ██████████████████████████     ETA: 4s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 9000/10000 [ 90%] ███████████████████████████    ETA: 3s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 9100/10000 [ 91%] ███████████████████████████    ETA: 3s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 9200/10000 [ 92%] ███████████████████████████    ETA: 3s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 9300/10000 [ 93%] ███████████████████████████    ETA: 2s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 9400/10000 [ 94%] ████████████████████████████   ETA: 2s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 9500/10000 [ 95%] ████████████████████████████   ETA: 1s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 9600/10000 [ 96%] ████████████████████████████   ETA: 1s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 9700/10000 [ 97%] █████████████████████████████  ETA: 1s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 9800/10000 [ 98%] █████████████████████████████  ETA: 0s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 9900/10000 [ 99%] █████████████████████████████  ETA: 0s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r10000/10000 [100%] ██████████████████████████████ Elapsed: 39s | Acceptance Rate: 1.000"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "# INFERENCE \n",
    "inference = ed.Gibbs(latent_vars={pheads: q_pheads},\n",
    "                    data={c: c_train})\n",
    "inference.run()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Inferred posterior mean:\n0.490163\nInferred posterior std:\n0.0493696\n"
     ]
    }
   ],
   "source": [
    "# CRITICISM\n",
    "mean, stddev = sess.run([q_pheads.mean(),q_pheads.stddev()])\n",
    "print('Inferred posterior mean:')\n",
    "print(mean)\n",
    "print('Inferred posterior std:')\n",
    "print(stddev)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x24a9d089dd8>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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GrFerbUWgjZvSdC/ZWru2sc1mzp/Q/ui6rOshijl3QsVfos+5jevPnftDrPZ2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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24a90d97048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(q_pheads.params.eval());\n",
    "plt.axhline(y=pheads_true)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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+DpK9+F9KX/hQV17rYjUACtGEOmZr1qzR7bffrquuusqpegAUCXt9WSBpqaoE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\ngEwIMwCATLwAupkxgd82B/kAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24a98d329e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = tf.range(0.0,1.0,0.001)\n",
    "plt.plot(*sess.run([x,pheads.prob(x)]));\n",
    "plt.plot(*sess.run([x,pheads_cond.prob(x)],\n",
    "                  {c:c_train}));\n",
    "plt.hist(q_pheads.params.eval(),\n",
    "        bins=100,range=(0.0,1.0),\n",
    "        normed = True);\n",
    "plt.axvline(x=pheads_true);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6dHGZ16FDB/n5+dU7hl3ttNpTu+4wDEPV1W4v3mTVdYpgtxuqruY/T2tHnVo/atQ2UKfW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\nc67t8duyO1Orvjqg8aN6anD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tvF0/EGvf38lXRSukvY82Jmbo1rEXOt2dZBiG3t94SB38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\neIH/AN+ePIkBcx4BAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24a989c6a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(lags(q_pheads.params).eval());"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## MCMC: Hamiltonian monte carlo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Metropolis hasting and Gibbs will fail in high_dimensional paramter space while HMC will not. \n",
    "\n",
    "HMC unitlises the geometry of the important regions of the posterior (where the probability mass is concentrated) to guide the jump proposal.\n",
    "\n",
    "For Gibbs you need to be able to derive the complete conditional algebraically. Most of the times this is not the case, so Gibbs cannot be used. Hamiltonian monte carlo does not have this restriction. However, it only works for continuous variables. This is because it works with derivatives (i.e. we need smooth functions).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# BACKWARD MODEL\n",
    "T = 10000 # number of empirical samples\n",
    "q_pheads = Empirical(params=tf.Variable(tf.ones([T])*.5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\r    1/10000 [  0%]                                ETA: 104024s | Acceptance Rate: nan"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r  100/10000 [  1%]                                ETA: 1180s | Acceptance Rate: 0.990"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r  200/10000 [  2%]                                ETA: 655s | Acceptance Rate: 0.980 "
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r  300/10000 [  3%]                                ETA: 479s | Acceptance Rate: 0.983"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r  400/10000 [  4%] █                              ETA: 389s | Acceptance Rate: 0.987"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r  500/10000 [  5%] █                              ETA: 336s | Acceptance Rate: 0.990"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r  600/10000 [  6%] █                              ETA: 301s | Acceptance Rate: 0.992"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r  700/10000 [  7%] ██                             ETA: 274s | Acceptance Rate: 0.993"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r  800/10000 [  8%] ██                             ETA: 255s | Acceptance Rate: 0.994"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r  900/10000 [  9%] ██                             ETA: 238s | Acceptance Rate: 0.993"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 1000/10000 [ 10%] ███                            ETA: 226s | Acceptance Rate: 0.994"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 1100/10000 [ 11%] ███                            ETA: 215s | Acceptance Rate: 0.995"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 1200/10000 [ 12%] ███                            ETA: 206s | Acceptance Rate: 0.994"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 1300/10000 [ 13%] ███                            ETA: 198s | Acceptance Rate: 0.995"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 1400/10000 [ 14%] ████                           ETA: 192s | Acceptance Rate: 0.995"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 1500/10000 [ 15%] ████                           ETA: 186s | Acceptance Rate: 0.995"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 1600/10000 [ 16%] ████                           ETA: 180s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 1700/10000 [ 17%] █████                          ETA: 175s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 1800/10000 [ 18%] █████                          ETA: 170s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 1900/10000 [ 19%] █████                          ETA: 166s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 2000/10000 [ 20%] ██████                         ETA: 162s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 2100/10000 [ 21%] ██████                         ETA: 158s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 2200/10000 [ 22%] ██████                         ETA: 154s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 2300/10000 [ 23%] ██████                         ETA: 150s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 2400/10000 [ 24%] ███████                        ETA: 147s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 2500/10000 [ 25%] ███████                        ETA: 142s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 2600/10000 [ 26%] ███████                        ETA: 137s | Acceptance Rate: 0.997"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 2700/10000 [ 27%] ████████                       ETA: 132s | Acceptance Rate: 0.997"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 2800/10000 [ 28%] ████████                       ETA: 128s | Acceptance Rate: 0.997"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 2900/10000 [ 28%] ████████                       ETA: 124s | Acceptance Rate: 0.997"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 3000/10000 [ 30%] █████████                      ETA: 120s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 3100/10000 [ 31%] █████████                      ETA: 116s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 3200/10000 [ 32%] █████████                      ETA: 112s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 3300/10000 [ 33%] █████████                      ETA: 109s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 3400/10000 [ 34%] ██████████                     ETA: 106s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 3500/10000 [ 35%] ██████████                     ETA: 104s | Acceptance Rate: 0.995"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 3600/10000 [ 36%] ██████████                     ETA: 102s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 3700/10000 [ 37%] ███████████                    ETA: 100s | Acceptance Rate: 0.995"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 3800/10000 [ 38%] ███████████                    ETA: 99s | Acceptance Rate: 0.996 "
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 3900/10000 [ 39%] ███████████                    ETA: 97s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 4000/10000 [ 40%] ████████████                   ETA: 95s | Acceptance Rate: 0.995"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 4100/10000 [ 41%] ████████████                   ETA: 93s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 4200/10000 [ 42%] ████████████                   ETA: 91s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 4300/10000 [ 43%] ████████████                   ETA: 89s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 4400/10000 [ 44%] █████████████                  ETA: 88s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 4500/10000 [ 45%] █████████████                  ETA: 86s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 4600/10000 [ 46%] █████████████                  ETA: 84s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 4700/10000 [ 47%] ██████████████                 ETA: 83s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 4800/10000 [ 48%] ██████████████                 ETA: 81s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 4900/10000 [ 49%] ██████████████                 ETA: 79s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 5000/10000 [ 50%] ███████████████                ETA: 78s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 5100/10000 [ 51%] ███████████████                ETA: 76s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 5200/10000 [ 52%] ███████████████                ETA: 74s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 5300/10000 [ 53%] ███████████████                ETA: 73s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 5400/10000 [ 54%] ████████████████               ETA: 71s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 5500/10000 [ 55%] ████████████████               ETA: 70s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 5600/10000 [ 56%] ████████████████               ETA: 68s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 5700/10000 [ 56%] █████████████████              ETA: 67s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 5800/10000 [ 57%] █████████████████              ETA: 65s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 5900/10000 [ 59%] █████████████████              ETA: 63s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 6000/10000 [ 60%] ██████████████████             ETA: 62s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 6100/10000 [ 61%] ██████████████████             ETA: 60s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 6200/10000 [ 62%] ██████████████████             ETA: 58s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 6300/10000 [ 63%] ██████████████████             ETA: 57s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 6400/10000 [ 64%] ███████████████████            ETA: 55s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 6500/10000 [ 65%] ███████████████████            ETA: 54s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 6600/10000 [ 66%] ███████████████████            ETA: 52s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 6700/10000 [ 67%] ████████████████████           ETA: 50s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 6800/10000 [ 68%] ████████████████████           ETA: 49s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 6900/10000 [ 69%] ████████████████████           ETA: 47s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 7000/10000 [ 70%] █████████████████████          ETA: 45s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 7100/10000 [ 71%] █████████████████████          ETA: 44s | Acceptance Rate: 0.996"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 7200/10000 [ 72%] █████████████████████          ETA: 42s | Acceptance Rate: 0.997"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 7300/10000 [ 73%] █████████████████████          ETA: 41s | Acceptance Rate: 0.997"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 7400/10000 [ 74%] ██████████████████████         ETA: 39s | Acceptance Rate: 0.997"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 7500/10000 [ 75%] ██████████████████████         ETA: 38s | Acceptance Rate: 0.997"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 7600/10000 [ 76%] ██████████████████████         ETA: 36s | Acceptance Rate: 0.997"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 7700/10000 [ 77%] ███████████████████████        ETA: 35s | Acceptance Rate: 0.997"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 7800/10000 [ 78%] ███████████████████████        ETA: 33s | Acceptance Rate: 0.997"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 7900/10000 [ 79%] ███████████████████████        ETA: 32s | Acceptance Rate: 0.997"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 8000/10000 [ 80%] ████████████████████████       ETA: 30s | Acceptance Rate: 0.997"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 8100/10000 [ 81%] ████████████████████████       ETA: 29s | Acceptance Rate: 0.997"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 8200/10000 [ 82%] ████████████████████████       ETA: 27s | Acceptance Rate: 0.997"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 8300/10000 [ 83%] ████████████████████████       ETA: 26s | Acceptance Rate: 0.997"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 8400/10000 [ 84%] █████████████████████████      ETA: 24s | Acceptance Rate: 0.997"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 8500/10000 [ 85%] █████████████████████████      ETA: 22s | Acceptance Rate: 0.997"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 8600/10000 [ 86%] █████████████████████████      ETA: 21s | Acceptance Rate: 0.997"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 8700/10000 [ 87%] ██████████████████████████     ETA: 19s | Acceptance Rate: 0.997"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 8800/10000 [ 88%] ██████████████████████████     ETA: 18s | Acceptance Rate: 0.997"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 8900/10000 [ 89%] ██████████████████████████     ETA: 16s | Acceptance Rate: 0.997"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 9000/10000 [ 90%] ███████████████████████████    ETA: 15s | Acceptance Rate: 0.997"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 9100/10000 [ 91%] ███████████████████████████    ETA: 13s | Acceptance Rate: 0.997"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 9200/10000 [ 92%] ███████████████████████████    ETA: 12s | Acceptance Rate: 0.997"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 9300/10000 [ 93%] ███████████████████████████    ETA: 10s | Acceptance Rate: 0.997"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 9400/10000 [ 94%] ████████████████████████████   ETA: 9s | Acceptance Rate: 0.997 "
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 9500/10000 [ 95%] ████████████████████████████   ETA: 7s | Acceptance Rate: 0.997"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 9600/10000 [ 96%] ████████████████████████████   ETA: 6s | Acceptance Rate: 0.997"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 9700/10000 [ 97%] █████████████████████████████  ETA: 4s | Acceptance Rate: 0.997"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 9800/10000 [ 98%] █████████████████████████████  ETA: 3s | Acceptance Rate: 0.997"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r 9900/10000 [ 99%] █████████████████████████████  ETA: 1s | Acceptance Rate: 0.997"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r10000/10000 [100%] ██████████████████████████████ Elapsed: 153s | Acceptance Rate: 0.997"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "# INFERENCE\n",
    "inference = ed.HMC(latent_vars={pheads: q_pheads},\n",
    "                  data = {c: c_train})\n",
    "inference.run(step_size=1.0 / N, n_steps=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Inferred posterior mean:\n",
      "0.539722\n",
      "Inferred posterior stddev\n",
      "0.0492454\n"
     ]
    }
   ],
   "source": [
    "# criticism\n",
    "mean, stddev = sess.run([q_pheads.mean(), q_pheads.stddev()])\n",
    "print(\"Inferred posterior mean:\")\n",
    "print(mean)\n",
    "print(\"Inferred posterior stddev\")\n",
    "print(stddev)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    ""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x120748278>"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Idmo7nptnKU7dkIu/jDjiLLHr3DjKkUMideBnyd6UCwCMh6xzFanugx3f5wMAvk275NyG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\ngz8iIiIiN8Lgj4iIiMiN/H9rQf+T+CvFigAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1207482b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(q_pheads.params.eval())\n",
    "plt.axhline(y=pheads_true)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x125178da0>]"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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XhxtrPZSXl0WhoUHKzi6gRh6MOnk+atQ0UCfPd75r1KpVcJXbG3hSFAAAAHgSwh8AAICJ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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12567ff60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(lags(q_pheads.params).eval())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x12541f908>"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Qg50yDuGAl4z6E/3WW2/pwAMP1Pe///1C1AMAo1Zq05d1dMoATxpVKEulUvrq\nV7+qZDJZqHoAYFTi6YSiVaWxR5nFCp+xKr9iqbjN1QCYKKMKZcuXL9eaNWsKVQsAjNrQyw15fY8y\nS/2QadruCHuVAV6RdyhbvXq1br/9dl1++eWFrAcARqVnyAaqdR6/xJJl6PvsivTYWAmAiZRXKLOm\nLY855hidfvrpha4JAPJmhbLaSFplpdEoU5kh1UQzwYxOGeAdZfncacWKFVq/fr1+/OMfK5VKFbom\nAMhbT3b6sr5Ezry01IcNRaoDmU5Z08j3B+B8I4ayNWvW6Ec/+pH+8z//U1OnTtXGjRvH9EI+n0/+\nIpy97ff7dvgTzsMYuYNbxqk3nukUlcoif0t9JK1tKldXuNfxY1Tq3PJZKmVOGaNhQ1k6ndbVV1+t\nQw89VOecc864Xqi1tVY+X/HebFNTbdFeC2PDGLmD08epP9UvqXS2w7BYJzV0RXocP0bIYJycz+4x\nGjaU3XnnnVq9erUeeOAB9fRkFpP292cOgLFYTD09Paqvr1d5efmIL9TdHS5ap6ypqVbBYFiGYRb+\nBTFqjJE7uGWctoe6JZXOmZeW+uxi/65Ij+PHqNS55bNUyoo9Ri0tdbu8fdhQ9re//U3JZFJnn332\nTt+77777dN999+nee+/VEUccMWIBpmkqXcRfZA3DVDrNX34nY4zcwcnjlDbSCsYzvyiW3PRlNoR2\nR3qVSqdlGkyNOZ2TP0vIsHuMhg1lV111Va4zZunq6tKXv/xlffSjH9VZZ52l/fffv6AFAsDuBOP9\nMsxMOCm56ctspyxppBRKhFVbtuvfvAG4x7Ch7MADD9zpNmuh//Tp03X00UcXpioAyMPQPcpKbvpy\nSAjtiQVVW0coA9yOq9kCcC0rlFUmDFWmSmtaqDpuKpCdZhl6VQMA7kUoA+BauT3KSmzqUpJ8Gnzf\nPYQywBPy2jx2qJkzZ2r16tWFqAUARmVwj7LSmrq01EcMBRt2nMYF4F50ygC4Vil3yiQ6ZYDXEMoA\nuJbVISq17TAs1qWlCGWANxDKALiSaZpDOmUlOn2ZDaO9TF8CnkAoA+BKoWRYSSMpaXDPrlJjhbL+\nREjJdNLmagCMF6EMgCvtuEdZiYayyGCHsCfOFCbgdoQyAK7UFc1cj7fCX66aWGntUWbZYQPZKFOY\ngNsRygC4UncsE8paqltUqld9LDOk5upGSYM/DwDuRSgD4Erd2enL1qpmmyux1+SaVkmDPw8A7kUo\nA+BK3dlCbQ/cAAAgAElEQVTpy9aqFpsrsdek2kwoYwNZwP0IZQBcyZqua60u7U4ZoQzwDkIZANcx\nTCO3Rxmdssz772ahP+B6hDIArtOfGFDKSEmiU2Z1yvoS/UpmfyYA3IlQBsB1hk7V0SlrzX3Nzv6A\nuxHKALiOtUdZVaBKNWXVNldjr7aawVDKGZiAu5XZXQAAjEb7JcvUPq9Gml+nuq4Brbn0YrtLslVF\noFyNFQ3qS/SzgSzgcnTKALhOf21AktQQKs0Lkb+Xta6OThngboQyAK7TV5cNZSV6zcv3Ggxl7OoP\nuBmhDIDr9GdDWWOIUCZJLdmrGrBXGeBuhDIArmL4pFBN5tBFpyzD6pRZe7cBcCcW+gNwlVC1X4Y/\ncwnyBjplenrJmYpMq5COb1IwFtQbn1mmMkOae8fddpcGYJTolAFwFWvqUpIawiz0l4aEU59PoZrA\n8HcG4FiEMgCuYp15WRUzVJEyba7GGeojgx3D/loO64Bb8ekF4CqcebmzsrRUE838PIZ2EgG4C6EM\ngKsM1LLIf1esqVyrkwjAfQhlAFylj+0wdskKqYQywL0IZQBcxQod9Szy30F9yAplHNYBt+LTC8A1\nUkYqt0cZnbIdWZ2yATplgGsRygC4Rk8sKPmye5SxpmwH1pqyUI1faY7sgCvx0QXgGkOv7Ugo21Hu\n5+HzaYC9ygBXIpQBcI2uaCaU1UTTKiOT7WBoSGVdGeBOfHIBuEZXtFuS1DhAInuvHfYqY10Z4Ep5\nh7KXX35ZF154oQ477DAdddRR+upXv6qurq5C1gYAO7A6ZU0s8t8l64zUATaQBVwpr1D26quv6oIL\nLlBPT4++8IUv6BOf+IT+9Kc/6bzzzlMoFCp0jQAgaUinjFC2S9YUZh+dMsCVyvK50/e+9z3V19fr\n/vvvV2NjoyTpoIMO0mc+8xmtXLlSy5YtK2SNACDTNAllI7AuTN5fx8oUwI1G/OQmk0nV1dXpzDPP\nzAUySTrssMMkSatXry5cdQCQFUqGFUvHJbGmbHessNrH9CXgSiN2ysrLy7V8+fKdbn/zzTclSdOn\nT5/4qgDgPawumUSnbHesn0ukOqB4OqHKQIXNFQEYjVH3uLdt26bf/va3uvLKKzVp0iR9/OMfL0Rd\nALCDzmwoq0gaqo6bNlfjTENPgOiO9gxzTwBOlNeaMothGFq0aJGSyaQCgYC+973vadKkSXk91ufz\nyV+EZQ5+v2+HP+E8jJE7OG2cerIbxzYOpOWMipynLmLIb5gy/D51x7s1q3Ga3SVBzvssYWdOGaNR\nhbJUKqXvfOc78vv9evjhh/WlL31JXV1deS30b22tlc9XvDfb1FRbtNfC2DBG7uCUcepb0yeJqcvh\n+E2pPpxWX32ZIr6QWlrq7C4JQzjls4Tds3uMRhXKKioqdPrpp0uSPvKRj+jcc8/VLbfcorPOOkt1\ndcN/+Lu7w0XrlDU11SoYDMswmOJwIsbIHZw2TpuC2yQRykbSNJAJZeu7t6inhy2LnMBpnyXsrNhj\ntLtfmEYVyoYKBAI65ZRTdMMNN2jt2rU66KCDhr2/aZpKF/FYahim0mn+8jsZY+QOThmnzgjbYeTD\n2hajM9ztiHHDIKd8lrB7do/RiL2rjo4OLVq0SD/5yU92+l44HJYkVVVVTXxlAJCVSCfUnxiQxHYY\nI7EW+3fFuke4JwCnGTGUzZw5U7FYTD//+c9zIUyS+vr69Mgjj2jWrFnaZ599ClokgNLWNeRMQjpl\nw7M6Zd3RXhmmYXM1AEZjxOlLn8+na6+9VldccYXOO+88nXXWWYrFYnrwwQfV29urFStWFHUBP4DS\nY22H4ff5VR8haAzHCq1pM63eWJ9aq5ttrghAvvJaen/iiSdq+fLlqq6u1g033KDly5dr33331YMP\nPqgjjzyy0DUCKHHWxrGtVc3ysyRnWI2hwdDazRQm4Cp5L/T/0Ic+pA996EMFLAUAds0KZW3VrTZX\n4nwVKVPVUUPRar86o92a28zyEsAtuGotAMezpi8nEcryklvsz67+gKsQygA4Hp2y0WnMhTKmLwE3\nIZQBcLS0kVZ3rFcSoSxfDYQywJUIZQAcrTs2uLXDlJo2m6txB6YvAXcilAFwtO2RTkmSTz610inL\ni9Upi6SiiiQjNlcDIF+EMgCOZi3yb6lqVrl/zFeGKylNQ6560MkUJuAahDIAjmZ1yiYzdZm3mpih\ncn+5JKYwATchlAFwtO2RLkmEstHwSWqrbpHEYn/ATQhlABxtezQbyqon2VyJu1hnqhLKAPcglAFw\nrEQ6qd5YUBKdstGalAtlTF8CbkEoA+BYXdFumcpc7JJQNjqt2elLFvoD7kEoA+BY1tRlwBdQS1Wz\nzdW4y5TsdG9vPKhEOmlzNQDywfnlAByp/ZJleuOAGmlBnRqDcb196afsLslVhnYWO6NdmlE3zcZq\nAOSDThkAx+ptCEjacd8t5Ke5qkll2X3drDNYATgboQyAYwXrs6GsP2VzJe7z9qWfUmNPTJL0xv/e\nrvZLltlbEIAREcoAOJYVyprplI1J00AmzPZmf44AnI1QBsCR4mU+RaqZvhyPpv7Mzy3YQCgD3IBQ\nBsCRgkO6O4SysbE6jMF6zukC3IBQBsCRrO5OedJQbdSwuRp3ssJstMqvWIXP5moAjIRQBsCRrHVQ\nTQNpESfGxlpTJu3YeQTgTIQyAI7U25CZcmPqcuxqYqYqEpkuYy9TmIDjEcoAOJK1R1lLP6FsrHwa\nDLUs9gecj1AGwHEM01BPtlPW0sceZeMxuNifUAY4HaEMgOP0xHqVLsusJCOUjY+18S57lQHORygD\n4Dhbw9slST7DZE3ZOA3tlJmmaXM1AIZDKAPgOFsjmVDWEE6rjN0wxsXaQDZZ7ldfot/magAMh1AG\nwHGsTllrH12y8RraaeTC5ICzEcoAOM7W8DZJUjPrycatMmWqJpoJZtsjnTZXA2A4hDIAjmKaZm76\nku0wJkZz9udo/VwBOBOhDICj9CcGFE3FJEkt/XTKJoL1c7SmhQE4E6EMgKMMDQ4trCmbENbPkVAG\nOFveoez555/XRRddpAULFmj+/Pn6+Mc/rqeeeqqQtQEoQVsimfVkdeG0KlJs4TARrL3eeuNBxbJd\nSADOk1co+9e//qVly5Zpy5Ytuvzyy/XFL35R4XBY//Zv/6bf//73ha4RQAnZFmY92UQb+rPcxmJ/\nwLHyukLtd77zHTU2NmrlypVqaGiQJJ177rk67bTTdP311+vkk08uaJEASoc1xcZO/hOnNmqoImEo\nUeHXlvA27dEwy+6SAOzCiJ2yWCym119/XYsWLcoFMkmqrq7WCSecoE2bNmnLli0FLRJA6Rg885JQ\nNlF8GtzzjXVlgHON2CmrqKjQE088ofLy8p2+19vbK0kKBLimGoDxiyQj6k8MSGKR/0Rr6Utpy6Ry\nbc2u2QPgPCOGMr/fr9mzZ+90+7Zt2/THP/5Rs2fP1uTJkwtSHIDS0H7JMknS5rYy6cMtkqRmOmUT\nyuo8bqFTBjhWXmvK3iuRSOgrX/mKotGoLrvssrwe4/P55C/CBhx+v2+HP+E8jJE72DFO3U2ZQ1J1\n1FBNnDMvJ5LVeeyO9iitlCoCO89+oDA45jmfU8Zo1KEsmUzqyiuv1LPPPqvFixfrzDPPzOtxra21\n8vmK92abmmqL9loYG8bIHYo5Tl3ZUNbGIv8JZ504YcpUrCykqc0s9i82jnnOZ/cYjSqURaNR/fu/\n/7ueeuopffCDH9R1112X92O7u8NF65Q1NdUqGAzLMPhN24kYI3ewY5xyoSxIKJto9RFDlYEKxdMJ\nvbV5nRrMZrtLKhkc85yv2GPU0lK3y9vzDmUDAwP6zGc+o5deekknnXSSbrrpJlVUVORdgGmaShdx\n3a5hmEqn+cvvZIyROxRrnEwNTl+2EsomnE/SlJrJ2jCwUZsHtio9mc9esXHMcz67xyiv3lUsFtOl\nl16ql156SR/72Md0yy23jCqQAcBIQjV+xSsyhyQ6ZYUxrXaKJC5MDjhVXqHsuuuu08svv6wlS5bo\nu9/9LltgAJhw1tSlzzDZOLZAyn6buTTe+rdfUfsly3JnvQJwhhGnLzs6OvTwww+rsrJShx12mH75\ny1/udJ9Fixaprm7X86MAkI/uxszhqDGUVjlblBWEtS1GsD6gtF8KGDYXBGAHI4ayF154QYZhKB6P\n65prrtnlfZ544glCGYBx6WpmkX+hWdtimH6feusDamODXsBRRgxlS5cu1dKlS4tRC4AS1tVIKCu0\nxlBa5UlDyXK/uprLCGWAwxRhkwoAGF7aL/U2ZNaqcuZl4Qy9Bqa1hg+AcxDKANiutz4gI5DZXLot\nSPemkNp6M6GXUAY4D6EMgO2s9WRlKVONIUJZIVnTw4QywHkIZQBs19mcuQ7jpN6UuDpgYVmhLFwT\nUKSSnzbgJIQyALbbnu2UTepN2lyJ9w09kaKbbhngKIQyALYyTVOdLZlwMLmHRf6FVpk0VR9isT/g\nRIQyALbqjvXmLq80qZdQVgyTst2yTkIZ4CiEMgC26hjYJEnyp021cnmlorCmMLubCWWAkxDKANjK\nCmVtfSku+1Mk1rYY3Y1lShuc7Qo4BaEMgK2sUDaJ9WRFY3XK0gGftke7bK4GgIVQBsA2pmkOhjLW\nkxWNdbklaTAUA7AfoQyAbfoS/RpIhiRJk3vYDqNY/ObgFOaGgY02VwPAQigDYBurS+MzTC5EXmRT\nstPFG/rplAFOQSgDYJsN2VDW3J9WOevNi8raE25jaJMMkzMsACcglAGwzbr+DZKkKd1MXRabNV0c\nTye0PdJpczUAJEIZAJuYpqn1/R2SpKmEsqJrHhhc7L+Bxf6AIxDKANiiM9qtcDIiSZrazXqyYvOb\ng2e8stgfcAZCGQBbWFOX5f5yFvnbZDKL/QFHIZQBsMW67NTl7PqZ8ps2F1OipmTXlXWw2B9wBEIZ\nAFus68t0yuY0zrK5ktJldcoSLPYHHIFQBqDokumkNoY2S5LmNMy2uZrS1TSQVmWgQpK0vp91ZYDd\nCGUAim5jaLPSZmZjsj0JZbbxm5npY0lam13jB8A+hDIARWetJ2usqFdTZaPN1ZS2vRrnSJLW9q23\ntxAAhDIAxfdu3zpJmalLn89nbzElbs/GTKdyU2iLYqmYzdUApY1QBqCoVl+yTKvXvSxJavj9s2q/\nZJm9BZW4PRv2kCSZMllXBtiMUAagqPrqAgrXBCRJMzrZyd9udRW1mlzdJkla288UJmAnQhmAoto0\nuVySVJ40cjvKw157Nma6Ze+yrgywFaEMQFFtnpQJZdO6kmwa6xDWurJ1fRtkmgwKYBdCGYCisjpl\nM7YzdekU1rqycCrCJrKAjQhlAIqmL96vvvoySYQyJ5leNzW3iSxTmIB9CGUAiubt4FpJUiBtako3\nocwp/D5/rltmjRGA4htTKPvmN7+pc845Z6JrAeBx1j/4U7qTKuP6146yb/PekqQ1wXdsrgQoXaMO\nZStXrtSDDz5YiFoAeNzq3rclMXXpRHOb95Ikdcd61R3tsbkaoDTlHcrS6bRuu+02feMb3yhkPQA8\nqjcW1LbIdknS7K0Jm6vBe+1RP0sV2XVl7cF3ba4GKE15hbJ4PK4zzjhDt956q5YsWaIpU6YUui4A\nHvNWzxpJUlnK1NQuOmVOE/AHtHf2OphrepnCBOxQls+d4vG4QqGQbr75Zp166qk64YQTCl0XAI95\nqzcTymZsT7CezEGGXuaq+X010iF1au99R6Zpcl1SoMjyCmV1dXX6wx/+oLKyvO5uq1Ta0JausIJ9\nERlpNkF0In/Ap7jhY4wcbiLHyTQNvdHdLkmatN2n3rK6iShxVPrKanf5NQY1dmUmT3rjQbVv26Tm\nyhabK/IGjnnO5w/4VN9QY3cZ+YUyv98vv398u2f4fD6N8ylGlEobuuonz6grGCvsCwEYFV9Nv6oO\njEiS/h44Xn+bU29rPQ/OPNnW13csn6Gq9J/lC6T1/V//RemumXZXBBTN5JYaXX/ZkQoE7OsQF631\n1dpaW/BWeDJljDs8Aph4gYYuSZKZqJQZLX6XDHky/TIGmhVo6pK/sYtQhpLT2Fir8jL7ckTRQll3\nd7jgnTJJuv6yI5U0/ervj8jgGm6O5Pf51NBQwxg53ESO0z2r2/XugHTItP01/xePTVCFo9NXVpvr\nkH184+/VmArbUofTvVlephcWVKh+cp++8uEj5Pfxi+54ccxzPr/Pp71mtyocisowCj9GLS27/uW0\naKHMNE2l04V/nUDAp2mttar0m0ozd+9IgYBPLS2MkdNN1DhFU1GtD2Uu3bNgyvvUmPrjRJU4Zo2p\nsJpTIbvLcKQDNgb0woJWRdNRhdSlvbI7/WPsOOY5XyDgU3mZX4Zh7xjxKxCAgnqje7XSZlp+n1/z\nWve3uxyMoHkgrbbqVknSG91v2VwNUFqcfzolAFf7V9cbkqR9m/ZSTXm1zdUgHzNe6VDXfjV68cXf\nae53fpa7fe4dd9tXFFAC6JQBKJi0kdaqbLfloLb32VwN8jVnc+aKC9tbyxWuYq8yoFgIZQAK5slr\nLlM0ldmipv6Gu3bYqBTONXN7QoFUZl3N+mmVNlcDlI4xTV/+5S9/meg6AHjQ2pmZf9DbepNqiLCN\nv1uUpTPBbP30Sq2bXqH3rWXvR6AY6JQBKAjTNPXOjEwo22sjFyB3G2vM1k2vUCpgczFAiSCUASiI\ntf3rNVCX+dd8n464zdVgtPbeGJdMU8lyv9ZNq7C7HKAkEMoAFMQLW1+RJLUEU2oLpmyuBqNVGzM0\nY3tSkvT27CqbqwFKA6EMwIRLG2m9tP1VSdJ+62Pi/D132jfb4Vw7o0Ip/rUACo6PGYAJt7r3bYWS\nmcsYzV3P1KVb7Z0NZYlyvzYwhQkUHKEMwIT757bM1OXUrqSaQkW4vhoKoi5qaNr2zIL/NbPZGgMo\nNEIZgAkVTyf0SudrkqT91rGVgttZU5jvzKxULEXXEygkQhmACfXitlcVTyfk9/m17wZCmdvtty4m\nv5E5C/PlbNgGUBiEMgAT6unNz0mS5rfNU23MtLkajFdN3NSemzIdsmc2v2BzNYC3EcoATJhNoS1a\n179BknTMjCNsrgYT5X3vZDqe7/St1fZIl83VAN5FKAMwYf626VlJUmtVi/Zr3sfmajBR5mxJqCaa\nOWHjuS3/tLkawLsIZQAmRDgZ0bPZf7CPnXGE/D4OL17hN6UDste/fGbLP5U2OKMWKASOmgAmxN83\nPaukkVSFv1zHTmfq0mvmvROTTz71JfpZ8A8UCKEMwLiljJSe2vi0JOmo6e9XTXmNzRVhojUPpDWv\ndX9J0pMdf7e5GsCbCGUAxu25LS+qLzEgn3z60Mxj7S4HBXL8rMzYruvfoHf71ttcDeA9ZXYXAMDd\nUkZKv3rxYakuoH3XRRV84EoF7S4KBbFf8z6aXjtVm8Nb9Yf1T+qyg5fZXRLgKXTKAIzLc1te1EBd\nQDJNHfF62O5yUEA+n08f3uN4SdJrXW+oY2CTzRUB3kIoAzBm8XRCT6z7k6TMhcdb+jkrz+sOnTJf\nk2vaJEm/Xfdnm6sBvIXpSwBj9ucNTykY75M/berI1+iSeV37JcskSYfsWaU/HNWgVztf17r+DZrT\nMNvewgCPoFMGYEyC8T79cf3/SZLmr4mqeYAuWanYb11MLcGUJOmRNb+WaXI5LWAiEMoAjMnD7Y8r\nYSRVU1atw1lLVlL8pnTsKyFJ0rt969i3DJggTF8CGLVXOl/Xq52vS5LO2Oejqkr82OaKUGxzNic0\ne0tCG6ZV6KHn71H5r3tUmcp0zObecbe9xQEuRacMwKi8csXFuv/5n0qSZm5NqPU/CWSlyCfpgy8O\nKJA2FaoJ6B+H1NpdEuB6hDIAeTNMQ384qkGR6oDKk4YWPT8gn91FwTYt/enc1PW/5tZow5RymysC\n3I1QBiBvf1r/lNZPr5QkfeifITWFWNxf6g59M6K23qQk6fdHNyhSSUwHxopQBiAv/+pcpV+++ztJ\n0n5rYzpgbczmiuAEAUP6yNP9KkuZilQH9LujG5U2COvAWBDKAIzo7eBa/fSNn8mUqcndSS16vp9p\nS+S09Kd1wgsDkqSOaRV6uP0XbJMBjAGhDMCw3g2u149fvVOJdEJNlY067a99KqcRgvc4YG1MC9+M\nSJL+vvk5/WbtHwlmwCixJQaA3Xrg3z6uJ45tVKLCr9pIWqf/6l3VRQ27y4JDHfNKSH11fr0zq0q/\nXfcnSaY+uueH5fPRVwXyQacMwE5M09RTHf/Q4x9qUqLCr+qooaV/CbJrP4blN6VTnu7XQW3vk5S5\nNuZD7b9QykjZXBngDnTKAOwglAzrwdWP6eXt/5L8PrUEUzr9qaAaw3TIMLIyQ/rgbf+nyDGNemdW\npf626Rm98/JTOvXv/Vpw2112lwc4Wt6dss2bN+uLX/yijjzySB166KG64oor1NHRUcjaABSRYRp6\nbsuL+vZzN2UCmaQ5m+I654+9BDKMSsCQTv17nw5dldnDbPPkCt23uEX/2PwC68yAYeTVKQsGg7rw\nwgsVCoV00UUXqby8XHfddZc+8YlP6Be/+IVaWloKXSeAAjFMQ691vaHfrvuzOgY2SZIq/OU6c+5i\nTXpgOWdZYkz8pnTsq2FN7k3pz4fXK17h1/1v/Vz/2PycFu91svZv2dfuEgHHySuU3X333dq4caNW\nrlypAw88UJJ07LHH6owzztCKFSt01VVXFbRIABOvO9qjF7e9qn9seV6d0e7c7Qe3zdMZ+3xU0+on\n6U0tt7FCeMHcDXFN70zq/w6r1zuzKrW2f4NufWWF5jTM1nEzjtTCyQerIlBhd5mAI+QVyn7961/r\nkEMOyQUySdp///11+OGH6ze/+Q2hDHCBRDqhdf0b9Mx9N2vD1AptbdvxkjiztiZ0+Othzdz+pIJ6\nUkGb6oT31EUNffRvfdowtVzPHFynbW3lWte/Qev6N+ih1Y/pgJa5OmjSPO3btJdaq5o5WxMla8RQ\n1tfXp46ODn3oQx/a6XsHHXSQnn32WW3fvl2TJ08uRH0A8mSapuLphELJkHpiveqOBdUT69W28HZt\nDG3W9kiXTJnSgYMXjq6KG9pnQ1wHr4lqUpAz5FA4Pkl7bE1q9tZebZhaodf2rdK7MyqVUFKvdq3S\nq12rJEn1FXXao36WptRO0tSayZpU3abGyno1VNSrMlBJYIOnjRjKtm3bJkmaMmXKTt+zgtiWLVsc\nEcpM09Qr21cp0hlWJBKXaey4oHS45aXmsN8d/jXH9LjhXm/Yb+3+m8NXMszjhn3gcK+36+8N/3Sm\nfH6fqjdXKBpN7DBGY65/hNcby+Oc9PfBMA2ljJSSRkpJI6mUkVbKSOb+P5KMKpyKKJKMKm2OvGVF\nc19Ks7YlNGdzQrO3JhRgDT+KKBPOEtpja0LhKp/WzqjUuzMr1TGlQqkynwYSIb3e/aZe735zp8dW\n+MtVX1GvqrJKVQYqVRmoyP1Z5g8o4AvI7/PL7/O/52u/fD5/bn2kz/pqSL7zvWf15K7Cn3Uf3453\nHPE9+30+1XRWKBJJyOBEB0fy+306umyBqlVnax0jhrJwOHP2THV19U7fs26LRCIjvpDP55O/wLui\nvRvcoJ+8ek9hXwRwibryWtVsDaoplFZbb0ptwZQm96RUGyOFwRlqY6YOfCemA9+JKe2TuprLtKWt\nXF1NZeptCKi3oUzRqsF/OBJGUt2xHhsrhpf9bdMz+v+OsXc51oihzPrNf7iWsT+PtNXWVvj02dIy\nTw/vdXvBXweAOy3OfbXExioAYNdGTFM1NTWSpGg0utP3rNvq6uxt9wEAALjdiKFsxowZkqTOzs6d\nvrd9+3ZJ0tSpUye4LAAAgNIyYiirr6/X7NmztWrVqp2+99prr2nGjBlqbW0tSHEAAAClIq+l96ec\ncopefPFFvfHGG7nb3nrrLT3//PNavHjxMI8EAABAPnxmHufwB4NBnXbaaUqlUvrUpz4lv9+vO++8\nU1VVVVq5ciWXWQIAABinvEKZJHV0dOi6667TM888o4qKCh1++OH6yle+olmzZhW6RgAAAM/LO5QB\nAACgcAq8nSsAAADy4apQtnnzZn3xi1/UkUceqUMPPVRXXHGFOjo6RnxcLBbT97//fR1//PGaP3++\nzj33XD3zzDNFqLj0jHWMNm7cqC996Us68sgjdeCBB+qUU07R3XffPebLFmF4Yx2noSKRiE488USd\nc845BaqytI11jNLptO68806dfPLJOvjgg/WRj3xE99xzjwyDKzkUwljHqaenR1dddZWOOOIIHXTQ\nQVq6dKn+8pe/FKFifPOb38z7uFXs/OCa6ctgMKizzjpLoVBIF110kcrLy3XXXXeprKxMv/jFL4Y9\n2eCKK67Qk08+qfPPP1977bWXfv7zn6u9vV333HOPDjvssCK+C28b6xgNDAzotNNOU39/vy644AJN\nmTJFf/3rX/Xkk0/qggsu0De+8Y0ivxNvG89naahvfetb+t///V/Nnz9fDz/8cIGrLi3jGaOvf/3r\nWrlypZYuXaqDDz5Yf/3rX/WXv/xFn//85/W5z32uiO/C+8Y6TolEQkuXLtXatWv1iU98QrNnz9Yj\njzyiN998U7fddptOPPHEIr+T0rFy5Up9/etfz/u4VfT8YLrEzTffbO63337ma6+9lrvtzTffNPff\nf3/zu9/97m4f949//MOcO3eu+dOf/jR3WygUMo8//nhz6dKlhSy55Ix1jG666SZz7ty55gsvvLDD\n7f/xH/9h7rfffub69esLVnMpGus4DfX888+b+++/vzlv3jzz7LPPLlSpJWusY/Tss8+ac+fONW+8\n8cYdbv/0pz9tHnTQQWY0Gi1YzaVorOP0m9/8xpw7d665fPny3G0DAwPmMcccYy5evLigNZeqVCpl\n3nrrreZ+++1nzp07N6/jlh35wTXTl7/+9a91yCGH6MADD8zdtv/+++vwww/Xb37zm90+7le/+pXK\ny5WvF8EAAAeiSURBVMt3aFXW1tbqzDPP1Ouvv67169cXtO5SMtYxev7557XHHnvs9FvHRz/6UZmm\nqZdeeqlgNZeisY6TJRqN6mtf+5qWLl2qyZMnF7LUkjXWMXrkkUdUV1enz372szvcfvnll+vSSy9V\nKBQqWM2laKzjZE1vHnPMMbnb6urqtHDhQq1Zs4ap5gkWj8d1xhln6NZbb9WSJUs0ZcqUvB5nR35w\nRSjr6+tTR0fHDn/xLQcddJC2bduWu+TTe73++uvac889c9fwHPo4KXNVAozfeMboBz/4gW6/fecL\nyff29kqSysrKJrbYEjaecbLceOONisViuvrqqwtVZkkbzxj985//1MKFC1VdXS0ps+7PMAwtXLhQ\nn//859XW1lbQ2kvJeMZpzpw5kqR169btcHtHR4fa2trk97vin2bXiMfjCoVCuvnmm3X99dfn/W+K\nHfnBFSO/bds2SdplurV+U9+yZctuH7ura3Naj9u8efNElVnSxjNGU6ZM0d57773DbaZp6oEHHpDf\n79fChQsnuNrSNZ5xkjL/6N9///269tprVV9fX5giS9xYxygej2vz5s2aNm2aHn/8cZ100klasGCB\nDjvsMF1//fVKpVKFLbzEjOeztGjRIh133HG64YYb9PTTT6ujo0M33HCD3njjDV122WWFK7pE1dXV\n6Q9/+INOPfXUUT3OjvzgihZEOByWpNxvf0MN/Y1wd48d7nHRaHSiyixp4xmjXbnlllv0xhtv6GMf\n+5imT58+MUViXOMUi8X0ta99TaeeeqpOOOGEwhVZ4sY6RqFQSKZp6rnnntOvfvUrXXbZZZozZ47+\n/Oc/66677lIwGNR1111X2OJLyHg+S2VlZfrc5z6nL3zhC/rUpz6Vu/2Tn/ykPvnJTxag2tLm9/vH\n1H20Iz+4IpSZ2RNEfT7fbu8z1nYvbeKJMZFj9NOf/lS333679tprL868nGDjGaebbrpJoVBIX//6\n1wtSGzLGOkaJREJSZkpsxYoV+sAHPiBJOvnkk2Waph599FF9+tOf1j777FOAqkvPeD5Lf/vb33TZ\nZZeptbVV11xzjSZPnqy///3vuv/++xWJRAjPLlGI/OCKUGbN5+4qlVq31dXV7faxsVhs1I/D6Ixn\njIa69dZbddttt2nmzJm66667mCKbYGMdp5deekn33XefrrnmGkmZPZYkyTAMpVIp9fT0qLq6epe/\nVWJ0xjpG1s9+2rRpuUBmWbp0qX75y1/queeeI5RNkPEc82699VaVl5fr/vvvz12q8MMf/rCmTZum\nH/zgBzrppJPoRjuAHfnBFW2iGTNmSJI6Ozt3+p61kHJX876SNH369GEfl+9ZGBjeeMZIyvzW+d//\n/d+67bbbtOeee+qBBx7QtGnTClNsCRvrOD399NMyDEPXXnutjjrqqNx/W7Zs0apVq3TUUUfpjjvu\nKGzxJWKsY9TY2Kiamppd7o1l3WZNuWH8xnPMa29v18KFC3e6dvTSpUslSc8+++xElooxsiM/uKJT\nVl9fr9mzZ2vVqlU7fe+1117TjBkz1NrausvHzps3T7/85S8Vi8VUVVW1w+Mk6eCDDy5M0SVmPGMk\nSdddd53uu+8+HXDAAbrzzjuHvS/Gbqzj9LGPfUyHHnroTrd/+ctfVmNjo77xjW/s9A8MxmasY+Tz\n+XTAAQeovb1dyWRS5eXlue9ZWzDwi87EGc8xr7KyUul0eqfbrSlRtsRwBjvygys6ZZJ0yimn6MUX\nX9Qbb7yRu+2tt97S888/r8WLFw/7uEQioYceeih3Wzgc1iOPPKIFCxZo5syZBa27lIx1jJ544gnd\nc889mjt3ru655x4CWYGNZZxmzZqlo48+eqf/KisrVVdXp6OPPppQNoHG+lk67bTTNDAwoJ/97Ge5\n2wzD0L333quqqqqdpjUxPmMdp2OOOUYvvvii2tvbd7j9wQcflCQdeeSRhSkYo2JHfnDVZZZOO+00\npVIpfepTn5Lf79edd96pqqoqrVy5Ui0tLerq6tLTTz+t2bNna8GCBbnHXnLJJXrmmWd0wQUXaM6c\nOXrooYe0Zs0a3XPPPbv87R9jM5YxMk1TJ510kjo6OnTZZZdpr7322ul558+fn9vXB+M3ns/Se51w\nwglqa2vjMksTbKxjlEqldNFFF+mll17Sueeeq7lz5+oPf/iDnnnmGX3ta1/TRRddZPM785axjtPG\njRt19tlnK51O6/zzz9fUqVP13HPP6YknntAHP/hBLV++fNgTCDA+uzpuOSY/FOQ6AQWyYcMG87Of\n/ax5yCGHmIcffrj5uc99ztywYUPu+9YlRq666qodHhcKhcxvfetb5lFHHWUecsgh5rnnnms+++yz\nxS6/JIx2jDo6Osy5c+cO+98DDzxg19vxrLF+lt7r+OOP5zJLBTLWMQqHw+YNN9xgfuADHzAPPPBA\n87TTTjMfe+yxYpdfMsY6Th0dHeb/+3//zzziiCPMefPmmSeddJJ52223mYlEothvoeTs6rjllPzg\nmk4ZAACAl7lmTRkAAICXEcoAAAAcgFAGAADgAIQyAAAAByCUAQAAOAChDMD/324dCwAAAAAM8ree\nxo6iCIABKQMAGJAyAIABKQMAGJAyAICBAENOQlfUzJ7zAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118a56f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = tf.range(0.0, 1.0, 0.001)\n",
    "plt.plot(*sess.run([x, pheads.prob(x)]))\n",
    "plt.plot(*sess.run([x, pheads_cond.prob(x)],\n",
    "                  {c:c_train}))\n",
    "plt.hist(q_pheads.params.eval(),\n",
    "        bins=100, range=(0.0, 1.0),\n",
    "        normed=True)\n",
    "plt.axvline(x=pheads_true)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## variational inference (VI)\n",
    "\n",
    "Good alternative to markov chain monte carlo methods. Class of algorithm that cast posterior inference as optimisation:\n",
    "\n",
    "Approximate the model paramters, that is, the posterior p(params|data = obs):\n",
    "\n",
    "a. build a variational backward model, q(params: lambda), over the params with some variational paramters lambda.\n",
    "\n",
    "b. Match q(params; lambda) to p(params|obs) by optimising over lambda, \n",
    "\n",
    "lambda* = argmin Closeness(p(params|obs), q(params;lambda))\n",
    "\n",
    "c. use q(params;lambda*) instead of p(params|obs)\n",
    "\n",
    "d. criticise the variational model, revise it (-->a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# BACKWARD MODEL\n",
    "q_pheads_concentration1 = tf.nn.softplus(tf.Variable(51+ tf.random_normal([])))\n",
    "q_pheads_concentration0 = tf.nn.softplus(tf.Variable(51+ tf.random_normal([])))\n",
    "q_pheads = Beta(concentration1=q_pheads_concentration1,\n",
    "               concentration0=q_pheads_concentration0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x11eb5a940>]"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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m39BbQzKSTE4EtL5ml7JNmzbpjjvu0KBBgzRgwADNmjVLn3/+uTezAQCCwJdZ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\ngA+glAEAAPiA/w80PR08E6mtaQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12e9d0710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = tf.range(-5.0, 5.0, 0.001)\n",
    "plt.plot(*sess.run([x,tf.nn.softplus(x)]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1000/1000 [100%] ██████████████████████████████ Elapsed: 28s | Loss: 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     ]
    }
   ],
   "source": [
    "# inference\n",
    "inference = ed.KLqp(latent_vars={pheads: q_pheads},\n",
    "                   data={c:c_train})\n",
    "inference.run(n_samples=20, n_iter=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    ""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    ""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'concentration0': 46.225704, 'concentration1': 57.310051}"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sess.run({key: val for key, val in six.iteritems(q_pheads.parameters) if isinstance(val,tf.Tensor)})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x134e89c18>"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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KCtZBWSCp9ypjA1kiT2FQRkSetla2yWBkypzQo8xgZMpylTyKFr3K/CmjgSwz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\nTAghhBDCD0hRJoQQQgjhB/4/pHCNG2S8RzMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11e78d6a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(*sess.run([x,pheads.prob(x)]))\n",
    "plt.plot(*sess.run([x, pheads_cond.prob(x)],\n",
    "                  {c:c_train}))\n",
    "plt.plot(*sess.run([x, q_pheads.prob(x)]))\n",
    "plt.axvline(x=pheads_true)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Inferred posterior mean:\n",
      "0.553529\n",
      "Inferred posterior stddev\n",
      "0.0486222\n"
     ]
    }
   ],
   "source": [
    "# criticism\n",
    "mean, stddev = sess.run([q_pheads.mean(),q_pheads.stddev()])\n",
    "print(\"Inferred posterior mean:\")\n",
    "print(mean)\n",
    "print(\"Inferred posterior stddev\")\n",
    "print(stddev)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
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   "source": [
    "## A/B/... Testing"
   ]
  },
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   "execution_count": null,
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    "collapsed": false
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   "source": [
    ""
   ]
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   "metadata": {},
   "source": [
    "# Bayesian linear regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    ""
   ]
  }
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