nima.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import importlib.util\n",
    "import math\n",
    "import os.path\n",
    "from os import path\n",
    "import time\n",
    "\n",
    "from fastai.script import *\n",
    "from fastai.vision import *\n",
    "from fastai.callbacks import *\n",
    "from fastai.distributed import *\n",
    "from fastai.callbacks.tracker import *\n",
    "from fastai.utils.ipython import * \n",
    "torch.backends.cudnn.benchmark = True\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from torch import nn\n",
    "\n",
    "# from PIL import ImageFile\n",
    "# ImageFile.LOAD_TRUNCATED_IMAGES = True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv('./labels.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "255530"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>image_name</th>\n",
       "      <th>tags</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>953619</td>\n",
       "      <td>0 1 5 17 38 36 15 6 5 1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>953958</td>\n",
       "      <td>10 7 15 26 26 21 10 8 1 2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>954184</td>\n",
       "      <td>0 0 4 8 41 56 10 3 4 0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>954113</td>\n",
       "      <td>0 1 4 6 48 37 23 5 2 2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>953980</td>\n",
       "      <td>0 3 6 15 57 39 6 1 1 1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   image_name                       tags\n",
       "0      953619    0 1 5 17 38 36 15 6 5 1\n",
       "1      953958  10 7 15 26 26 21 10 8 1 2\n",
       "2      954184     0 0 4 8 41 56 10 3 4 0\n",
       "3      954113     0 1 4 6 48 37 23 5 2 2\n",
       "4      953980     0 3 6 15 57 39 6 1 1 1"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "tfms = ([\n",
    "    flip_lr(p=0.5),\n",
    "    brightness(change=(0.4,0.6)),\n",
    "    contrast(scale=(0.7,1.3))\n",
    "], [])\n",
    "\"\"\"\n",
    "tfms = ([], [])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "scores_map = dict(zip(df.image_name, df.tags))\n",
    "labels = list(scores_map.keys())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "50000\n",
      "100000\n",
      "150000\n",
      "200000\n",
      "250000\n"
     ]
    }
   ],
   "source": [
    "from PIL import Image\n",
    "assets_not_on_disk = []\n",
    "corrupt_images = [440774, 179118, 371434, 277832, 230701, 729377]\n",
    "for i, img_id in enumerate(labels):\n",
    "    if (i % 50000 == 0):\n",
    "        print(i) \n",
    "    if not (os.path.exists(os.path.join('./data', str(img_id)+'.jpg'))):\n",
    "        assets_not_on_disk.append(img_id)\n",
    "    elif (os.stat(os.path.join('./data', str(img_id)+'.jpg')).st_size/1024 < 50): #img size is < 50KB\n",
    "       corrupt_images.append(img_id)\n",
    "    # else:\n",
    "    #    try:\n",
    "    #        img=Image.open(os.path.join('./data', str(img_id)+'.jpg'))\n",
    "    #        img.transpose(PIL.Image.FLIP_LEFT_RIGHT)\n",
    "    #    except:\n",
    "    #        print(f\"corrupt image:{img_id}\")\n",
    "    #        corrupt_images.append(img_id)\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(255530, 22, 21035)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(labels), len(assets_not_on_disk), len(corrupt_images)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total available images: 234473\n"
     ]
    }
   ],
   "source": [
    "print(f\"Total available images: {len(labels) - len(assets_not_on_disk) - len(corrupt_images)}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "missing_images = assets_not_on_disk + corrupt_images"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "21057"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(missing_images)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = df[~df.image_name.isin(missing_images)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(234474, 234473)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(df), (len(labels) - len(missing_images))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>image_name</th>\n",
       "      <th>tags</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>10</td>\n",
       "      <td>953417</td>\n",
       "      <td>0 0 0 5 32 50 23 10 3 1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>11</td>\n",
       "      <td>953777</td>\n",
       "      <td>0 3 2 3 13 40 35 21 8 3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>12</td>\n",
       "      <td>953756</td>\n",
       "      <td>0 2 3 9 35 50 20 5 2 2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>13</td>\n",
       "      <td>954195</td>\n",
       "      <td>0 1 7 26 56 23 6 1 0 2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>14</td>\n",
       "      <td>953903</td>\n",
       "      <td>0 1 4 5 33 50 17 9 3 2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    image_name                     tags\n",
       "10      953417  0 0 0 5 32 50 23 10 3 1\n",
       "11      953777  0 3 2 3 13 40 35 21 8 3\n",
       "12      953756   0 2 3 9 35 50 20 5 2 2\n",
       "13      954195   0 1 7 26 56 23 6 1 0 2\n",
       "14      953903   0 1 4 5 33 50 17 9 3 2"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "datablocks_data = list(zip(\n",
    "                        df.image_name.apply(\n",
    "                            lambda x: '{}.jpg'.format(x)), df.tags\n",
    "                       ))\n",
    "datablocks_df = pd.DataFrame(datablocks_data, columns = ['name', 'label'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>name</th>\n",
       "      <th>label</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>953417.jpg</td>\n",
       "      <td>0 0 0 5 32 50 23 10 3 1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>953777.jpg</td>\n",
       "      <td>0 3 2 3 13 40 35 21 8 3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>953756.jpg</td>\n",
       "      <td>0 2 3 9 35 50 20 5 2 2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>954195.jpg</td>\n",
       "      <td>0 1 7 26 56 23 6 1 0 2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>953903.jpg</td>\n",
       "      <td>0 1 4 5 33 50 17 9 3 2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         name                    label\n",
       "0  953417.jpg  0 0 0 5 32 50 23 10 3 1\n",
       "1  953777.jpg  0 3 2 3 13 40 35 21 8 3\n",
       "2  953756.jpg   0 2 3 9 35 50 20 5 2 2\n",
       "3  954195.jpg   0 1 7 26 56 23 6 1 0 2\n",
       "4  953903.jpg   0 1 4 5 33 50 17 9 3 2"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "datablocks_df.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# datablocks_df = datablocks_df.head(100000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Recompute labels since key is has .jpg extension\n",
    "scores_map = dict(zip(datablocks_df.name, datablocks_df.label))\n",
    "labels = list(datablocks_df.name)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "234474"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "class NimaLabelList(CategoryList):\n",
    "    _processor=None\n",
    "    def __init__(self, items:Iterator, classes=labels, label_delim:str=None, **kwargs):\n",
    "        super().__init__(items, classes=classes, **kwargs)\n",
    "\n",
    "    def get(self, i):\n",
    "        dist = scores_map[self.items[i]]\n",
    "        dist = np.array(dist.split(' '), dtype=float)\n",
    "        dist = dist/dist.sum()\n",
    "        return dist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "func = lambda o: o.split('/')[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = (ImageList.from_df(datablocks_df, path='./data')\n",
    "        .split_by_rand_pct()\n",
    "        .label_from_func(func, label_cls=NimaLabelList)\n",
    "        .transform(tfms, size=224)\n",
    "        .databunch(bs=64))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ImageDataBunch;\n",
       "\n",
       "Train: LabelList (187580 items)\n",
       "x: ImageList\n",
       "Image (3, 224, 224),Image (3, 224, 224),Image (3, 224, 224),Image (3, 224, 224),Image (3, 224, 224)\n",
       "y: NimaLabelList\n",
       "[0.       0.       0.       0.040323 0.258065 0.403226 0.185484 0.080645 0.024194 0.008065],[0.       0.015625 0.023438 0.070312 0.273438 0.390625 0.15625  0.039062 0.015625 0.015625],[0.       0.008197 0.057377 0.213115 0.459016 0.188525 0.04918  0.008197 0.       0.016393],[0.       0.008065 0.032258 0.040323 0.266129 0.403226 0.137097 0.072581 0.024194 0.016129],[0.       0.007937 0.015873 0.031746 0.142857 0.325397 0.230159 0.134921 0.079365 0.031746]\n",
       "Path: data;\n",
       "\n",
       "Valid: LabelList (46894 items)\n",
       "x: ImageList\n",
       "Image (3, 224, 224),Image (3, 224, 224),Image (3, 224, 224),Image (3, 224, 224),Image (3, 224, 224)\n",
       "y: NimaLabelList\n",
       "[0.012945 0.029126 0.048544 0.100324 0.148867 0.15534  0.171521 0.148867 0.090615 0.093851],[0.021472 0.06135  0.153374 0.248466 0.282209 0.141104 0.055215 0.021472 0.009202 0.006135],[0.038647 0.038647 0.135266 0.246377 0.362319 0.120773 0.024155 0.009662 0.004831 0.019324],[0.005076 0.015228 0.025381 0.106599 0.274112 0.248731 0.192893 0.06599  0.055838 0.010152],[0.018349 0.03211  0.073394 0.261468 0.302752 0.188073 0.06422  0.036697 0.013761 0.009174]\n",
       "Path: data;\n",
       "\n",
       "Test: None"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "234474"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "data.c = 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "x,y = next(iter(data.train_dl))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(64, 64)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(x), len(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "# data.show_batch(rows=5, figsize=(9,7))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "# (input, target)\n",
    "def emd(y_hat, y):\n",
    "    cdf_y = torch.cumsum(y, dim=-1)\n",
    "    cdf_y_hat = torch.cumsum(y_hat, dim=-1).double()\n",
    "    power = torch.pow((cdf_y - cdf_y_hat), 2)\n",
    "    emd = torch.sqrt(torch.mean(power, dim=-1))\n",
    "    return torch.mean(emd)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Transfer Learning using Mobilenet V2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "# learn = cnn_learner(data, models.resnet34, metrics=error_rate)\n",
    "learner = cnn_learner(\n",
    "    data,\n",
    "    models.mobilenet_v2,\n",
    "    pretrained=True,\n",
    "    loss_func=emd,\n",
    "    ps=0.75,\n",
    "    #opt_func=optim.SGD\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_hat = learner.model(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([64, 10]), torch.Size([64, 10]))"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_hat.shape, y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(5.7130, device='cuda:0', dtype=torch.float64, grad_fn=<MeanBackward0>)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "emd(y_hat, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([0.0000, 0.0179, 0.0298, 0.1190, 0.4226, 0.3274, 0.0655, 0.0119, 0.0060,\n",
       "         0.0000], device='cuda:0', dtype=torch.float64),\n",
       " tensor([0.0000, 0.0179, 0.0476, 0.1667, 0.5893, 0.9167, 0.9821, 0.9940, 1.0000,\n",
       "         1.0000], device='cuda:0', dtype=torch.float64))"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y[0], torch.cumsum(y[0], dim=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<function __main__.emd(y_hat, y)>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "learner.loss_func"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Freeze Mobilenet Layers and train only the last layer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: left;\">\n",
       "      <th>epoch</th>\n",
       "      <th>train_loss</th>\n",
       "      <th>valid_loss</th>\n",
       "      <th>time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>0.119096</td>\n",
       "      <td>0.081332</td>\n",
       "      <td>06:30</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with gpu_mem_restore_ctx():\n",
    "    learner.fit_one_cycle(1)\n",
    "    #learner.fit(2, lr=[3e-7,3e-7, 3e-6]) # discriminative learning rates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "learner.save('stage-1')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "learner.load('stage-1');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LR Finder is complete, type {learner_name}.recorder.plot() to see the graph.\n"
     ]
    }
   ],
   "source": [
    "learner.lr_find()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "learner.recorder.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train entire model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: left;\">\n",
       "      <th>epoch</th>\n",
       "      <th>train_loss</th>\n",
       "      <th>valid_loss</th>\n",
       "      <th>time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>0.086095</td>\n",
       "      <td>0.085508</td>\n",
       "      <td>06:45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>0.087413</td>\n",
       "      <td>0.091290</td>\n",
       "      <td>06:53</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>0.089224</td>\n",
       "      <td>0.087246</td>\n",
       "      <td>06:58</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>0.089472</td>\n",
       "      <td>0.108424</td>\n",
       "      <td>07:02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>0.088316</td>\n",
       "      <td>0.087041</td>\n",
       "      <td>06:58</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>0.086829</td>\n",
       "      <td>0.086684</td>\n",
       "      <td>06:55</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>6</td>\n",
       "      <td>0.085305</td>\n",
       "      <td>0.225778</td>\n",
       "      <td>07:01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>7</td>\n",
       "      <td>0.081741</td>\n",
       "      <td>0.082199</td>\n",
       "      <td>06:59</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>8</td>\n",
       "      <td>0.080727</td>\n",
       "      <td>0.081699</td>\n",
       "      <td>07:05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9</td>\n",
       "      <td>0.080815</td>\n",
       "      <td>0.080772</td>\n",
       "      <td>07:09</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "learner.unfreeze()\n",
    "with gpu_mem_restore_ctx():\n",
    "    learner.fit_one_cycle(10, 3e-3)\n",
    "    # learner.fit(5, lr=[3e-7,3e-7, 3e-6]) # discriminative learning rates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "learner.save('stage-2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "pred = learner.model(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compare model distributions to actual distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "scores = np.arange(1,11)\n",
    "plt.plot(scores, y[0], label='target');\n",
    "plt.plot(scores, pred[0], label='model output');\n",
    "plt.title(\"PDF\")\n",
    "plt.xlabel(\"score buckets\")\n",
    "plt.ylabel(\"votes\");\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "scores = np.arange(1,11)\n",
    "plt.plot(scores, torch.cumsum(y[0], dim=-1), label='target');\n",
    "plt.plot(scores, torch.cumsum(pred[0], dim=-1), label='model output');\n",
    "plt.title(\"CDF\")\n",
    "plt.xlabel(\"scores\")\n",
    "plt.ylabel(\"votes cdf\");\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}