neural_networks.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import torch.optim as optim\n",
    "import torch.nn.functional as F"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Batch Normalization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[ 1.,  2.,  3.],\n",
      "        [ 4.,  5.,  6.],\n",
      "        [ 7.,  8.,  9.],\n",
      "        [10., 11., 12.]])\n",
      "tensor([[-0.8409, -0.2090, -1.3279],\n",
      "        [-0.2803, -0.0697, -0.4426],\n",
      "        [ 0.2803,  0.0697,  0.4426],\n",
      "        [ 0.8409,  0.2090,  1.3279]], grad_fn=<NativeBatchNormBackward>)\n"
     ]
    }
   ],
   "source": [
    "m = nn.BatchNorm1d(3)\n",
    "input = torch.tensor([[1, 2, 3],\n",
    "                      [4, 5, 6],\n",
    "                      [7, 8, 9],\n",
    "                      [10, 11, 12]], dtype=torch.float)\n",
    "output = m(input)\n",
    "print(input)\n",
    "print(output)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dropout"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[ 1.,  2.,  3.],\n",
      "        [ 4.,  5.,  6.],\n",
      "        [ 7.,  8.,  9.],\n",
      "        [10., 11., 12.]])\n",
      "tensor([[ 0.0000,  2.5000,  3.7500],\n",
      "        [ 5.0000,  6.2500,  7.5000],\n",
      "        [ 8.7500, 10.0000, 11.2500],\n",
      "        [12.5000,  0.0000,  0.0000]])\n"
     ]
    }
   ],
   "source": [
    "m = nn.Dropout(p=0.2)\n",
    "input = torch.tensor([[1, 2, 3],\n",
    "                      [4, 5, 6],\n",
    "                      [7, 8, 9],\n",
    "                      [10, 11, 12]], dtype=torch.float)\n",
    "output = m(input)\n",
    "print(input)\n",
    "print(output)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear Regression Example using Neural Network"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Generate Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([100])\n",
      "torch.Size([100])\n"
     ]
    }
   ],
   "source": [
    "x = 20 * torch.rand(100) - 10\n",
    "y = (2 * torch.pow(x, 2)) + 5\n",
    "noise_ratio = 0.2 * torch.rand(100) - 0.1\n",
    "y_range = torch.max(y) - torch.min(y)\n",
    "noise = noise_ratio * y_range\n",
    "y = y + noise\n",
    "print(x.size())\n",
    "print(y.size())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plot Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "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": [
    "plt.scatter(x.numpy(), y.numpy(), alpha=0.7, s=15)\n",
    "plt.axhline(0, color=\"black\", linestyle=\"--\", alpha=0.3, linewidth=1)\n",
    "plt.axvline(0, color=\"black\", linestyle=\"--\", alpha=0.3, linewidth=1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Build Neural Network Architecture\n",
    "<img src=\"./screenshots/linear_net_architecture.png\" alt=\"drawing\" width=\"500\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Net(nn.Module):\n",
    "    def __init__(self):\n",
    "        super(Net, self).__init__()\n",
    "        self.fc1 = nn.Linear(1, 32, bias=True)\n",
    "        self.fc2 = nn.Linear(32, 32, bias=True)\n",
    "        self.fc3 = nn.Linear(32, 1, bias=True)\n",
    "        self.dropout = nn.Dropout(p=0.4)\n",
    "        self.batchnorm = nn.BatchNorm1d(32)\n",
    "    \n",
    "    def forward(self, x):\n",
    "        x = self.fc1(x)\n",
    "        x = self.batchnorm(x)\n",
    "        x = F.relu(x)\n",
    "        x = self.dropout(x)\n",
    "        x = self.fc2(x)\n",
    "        x = self.batchnorm(x)\n",
    "        x = F.relu(x)\n",
    "        x = self.dropout(x)\n",
    "        x = self.fc3(x)\n",
    "        return x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Initialize Neural Network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "net = Net()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Training Loop\n",
    "<img src=\"./screenshots/neural_network_to_code.png\" alt=\"drawing\" width=\"800\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mseloss: 9185.8935546875\n",
      "mseloss: 718.7135620117188\n",
      "mseloss: 455.95318603515625\n",
      "mseloss: 531.474365234375\n",
      "mseloss: 556.8598022460938\n",
      "mseloss: 413.8025207519531\n",
      "mseloss: 363.5050964355469\n",
      "mseloss: 520.000244140625\n",
      "mseloss: 320.6081237792969\n",
      "mseloss: 389.1635437011719\n"
     ]
    }
   ],
   "source": [
    "criterion = nn.MSELoss()\n",
    "optimizer = optim.Adam(net.parameters(), lr=0.0003)\n",
    "#tranining loop\n",
    "net.train()\n",
    "for i in range(0, 200000):\n",
    "    optimizer.zero_grad()\n",
    "    output = net(x.resize_(100, 1))\n",
    "    #print(output)\n",
    "    loss = criterion(output, y.resize_(100, 1))\n",
    "    if i%20000 == 0:\n",
    "        print(\"mseloss:\", loss.item())\n",
    "        #print(list(net.parameters()))\n",
    "    loss.backward()\n",
    "    optimizer.step()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Evaluate Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "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": [
    "net.eval()\n",
    "plt.scatter(x.numpy().reshape(100), y.numpy().reshape(100), alpha=0.7, s=15)\n",
    "plt.axhline(0, color=\"black\", linestyle=\"--\", alpha=0.3, linewidth=1)\n",
    "plt.axvline(0, color=\"black\", linestyle=\"--\", alpha=0.3, linewidth=1)\n",
    "x_pred = np.linspace(-10, 10, 100)\n",
    "output = net(x.resize_(100, 1))\n",
    "plt.plot(x.numpy().reshape(100), output.detach().numpy().reshape(100), \"ro\")\n",
    "plt.show()"
   ]
  },
  {
   "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}