pytorch_ipynb/basic-ml/logistic-regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Deep Learning Models -- A collection of various deep learning architectures, models, and tips for TensorFlow and PyTorch in Jupyter Notebooks.\n",
    "- Author: Sebastian Raschka\n",
    "- GitHub Repository: https://github.com/rasbt/deeplearning-models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sebastian Raschka \n",
      "\n",
      "CPython 3.7.1\n",
      "IPython 7.2.0\n",
      "\n",
      "torch 1.0.0\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -a 'Sebastian Raschka' -v -p torch"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Runs on CPU or GPU (if available)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Model Zoo -- Logistic Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Implementation of *classic* logistic regression for binary class labels."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from io import BytesIO\n",
    "\n",
    "import torch\n",
    "import torch.nn.functional as F"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Preparing a toy dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x180 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "##########################\n",
    "### DATASET\n",
    "##########################\n",
    "\n",
    "ds = np.lib.DataSource()\n",
    "fp = ds.open('https://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data')\n",
    "\n",
    "x = np.genfromtxt(BytesIO(fp.read().encode()), delimiter=',', usecols=range(2), max_rows=100)\n",
    "y = np.zeros(100)\n",
    "y[50:] = 1\n",
    "\n",
    "np.random.seed(1)\n",
    "idx = np.arange(y.shape[0])\n",
    "np.random.shuffle(idx)\n",
    "X_test, y_test = x[idx[:25]], y[idx[:25]]\n",
    "X_train, y_train = x[idx[25:]], y[idx[25:]]\n",
    "mu, std = np.mean(X_train, axis=0), np.std(X_train, axis=0)\n",
    "X_train, X_test = (X_train - mu) / std, (X_test - mu) / std\n",
    "\n",
    "fig, ax = plt.subplots(1, 2, figsize=(7, 2.5))\n",
    "ax[0].scatter(X_train[y_train == 1, 0], X_train[y_train == 1, 1])\n",
    "ax[0].scatter(X_train[y_train == 0, 0], X_train[y_train == 0, 1])\n",
    "ax[1].scatter(X_test[y_test == 1, 0], X_test[y_test == 1, 1])\n",
    "ax[1].scatter(X_test[y_test == 0, 0], X_test[y_test == 0, 1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Low-level implementation with manual gradients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "device = torch.device(\"cuda:0\" if torch.cuda.is_available() else \"cpu\")\n",
    "\n",
    "\n",
    "def custom_where(cond, x_1, x_2):\n",
    "    return (cond * x_1) + ((1-cond) * x_2)\n",
    "\n",
    "\n",
    "class LogisticRegression1():\n",
    "    def __init__(self, num_features):\n",
    "        self.num_features = num_features\n",
    "        self.weights = torch.zeros(num_features, 1, \n",
    "                                   dtype=torch.float32, device=device)\n",
    "        self.bias = torch.zeros(1, dtype=torch.float32, device=device)\n",
    "\n",
    "    def forward(self, x):\n",
    "        linear = torch.add(torch.mm(x, self.weights), self.bias)\n",
    "        probas = self._sigmoid(linear)\n",
    "        return probas\n",
    "        \n",
    "    def backward(self, probas, y):  \n",
    "        errors = y - probas.view(-1)\n",
    "        return errors\n",
    "            \n",
    "    def predict_labels(self, x):\n",
    "        probas = self.forward(x)\n",
    "        labels = custom_where(probas >= .5, 1, 0)\n",
    "        return labels    \n",
    "            \n",
    "    def evaluate(self, x, y):\n",
    "        labels = self.predict_labels(x).float()\n",
    "        accuracy = torch.sum(labels.view(-1) == y) / y.size()[0]\n",
    "        return accuracy\n",
    "    \n",
    "    def _sigmoid(self, z):\n",
    "        return 1. / (1. + torch.exp(-z))\n",
    "    \n",
    "    def _logit_cost(self, y, proba):\n",
    "        tmp1 = torch.mm(-y.view(1, -1), torch.log(proba))\n",
    "        tmp2 = torch.mm((1 - y).view(1, -1), torch.log(1 - proba))\n",
    "        return tmp1 - tmp2\n",
    "    \n",
    "    def train(self, x, y, num_epochs, learning_rate=0.01):\n",
    "        for e in range(num_epochs):\n",
    "            \n",
    "            #### Compute outputs ####\n",
    "            probas = self.forward(x)\n",
    "            \n",
    "            #### Compute gradients ####\n",
    "            errors = self.backward(probas, y)\n",
    "            neg_grad = torch.mm(x.transpose(0, 1), errors.view(-1, 1))\n",
    "            \n",
    "            #### Update weights ####\n",
    "            self.weights += learning_rate * neg_grad\n",
    "            self.bias += learning_rate * torch.sum(errors)\n",
    "            \n",
    "            #### Logging ####\n",
    "            print('Epoch: %03d' % (e+1), end=\"\")\n",
    "            print(' | Train ACC: %.3f' % self.evaluate(x, y), end=\"\")\n",
    "            print(' | Cost: %.3f' % self._logit_cost(y, self.forward(x)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 001 | Train ACC: 0.000 | Cost: 5.581\n",
      "Epoch: 002 | Train ACC: 0.000 | Cost: 4.882\n",
      "Epoch: 003 | Train ACC: 1.000 | Cost: 4.381\n",
      "Epoch: 004 | Train ACC: 1.000 | Cost: 3.998\n",
      "Epoch: 005 | Train ACC: 1.000 | Cost: 3.693\n",
      "Epoch: 006 | Train ACC: 1.000 | Cost: 3.443\n",
      "Epoch: 007 | Train ACC: 1.000 | Cost: 3.232\n",
      "Epoch: 008 | Train ACC: 1.000 | Cost: 3.052\n",
      "Epoch: 009 | Train ACC: 1.000 | Cost: 2.896\n",
      "Epoch: 010 | Train ACC: 1.000 | Cost: 2.758\n",
      "\n",
      "Model parameters:\n",
      "  Weights: tensor([[ 4.2267],\n",
      "        [-2.9613]], device='cuda:0')\n",
      "  Bias: tensor([0.0994], device='cuda:0')\n"
     ]
    }
   ],
   "source": [
    "X_train_tensor = torch.tensor(X_train, dtype=torch.float32, device=device)\n",
    "y_train_tensor = torch.tensor(y_train, dtype=torch.float32, device=device)\n",
    "\n",
    "logr = LogisticRegression1(num_features=2)\n",
    "logr.train(X_train_tensor, y_train_tensor, num_epochs=10, learning_rate=0.1)\n",
    "\n",
    "print('\\nModel parameters:')\n",
    "print('  Weights: %s' % logr.weights)\n",
    "print('  Bias: %s' % logr.bias)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Evaluating the Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test set accuracy: 100.00%\n"
     ]
    }
   ],
   "source": [
    "X_test_tensor = torch.tensor(X_test, dtype=torch.float32, device=device)\n",
    "y_test_tensor = torch.tensor(y_test, dtype=torch.float32, device=device)\n",
    "\n",
    "test_acc = logr.evaluate(X_test_tensor, y_test_tensor)\n",
    "print('Test set accuracy: %.2f%%' % (test_acc*100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "##########################\n",
    "### 2D Decision Boundary\n",
    "##########################\n",
    "\n",
    "w, b = logr.weights, logr.bias\n",
    "\n",
    "x_min = -2\n",
    "y_min = ( (-(w[0] * x_min) - b[0]) \n",
    "          / w[1] )\n",
    "\n",
    "x_max = 2\n",
    "y_max = ( (-(w[0] * x_max) - b[0]) \n",
    "          / w[1] )\n",
    "\n",
    "\n",
    "fig, ax = plt.subplots(1, 2, sharex=True, figsize=(7, 3))\n",
    "\n",
    "ax[0].plot([x_min, x_max], [y_min, y_max])\n",
    "ax[1].plot([x_min, x_max], [y_min, y_max])\n",
    "\n",
    "ax[0].scatter(X_train[y_train==0, 0], X_train[y_train==0, 1], label='class 0', marker='o')\n",
    "ax[0].scatter(X_train[y_train==1, 0], X_train[y_train==1, 1], label='class 1', marker='s')\n",
    "\n",
    "ax[1].scatter(X_test[y_test==0, 0], X_test[y_test==0, 1], label='class 0', marker='o')\n",
    "ax[1].scatter(X_test[y_test==1, 0], X_test[y_test==1, 1], label='class 1', marker='s')\n",
    "\n",
    "ax[1].legend(loc='upper left')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Low-level implementation using autograd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def custom_where(cond, x_1, x_2):\n",
    "    return (cond * x_1) + ((1-cond) * x_2)\n",
    "\n",
    "\n",
    "class LogisticRegression2():\n",
    "    def __init__(self, num_features):\n",
    "        self.num_features = num_features\n",
    "        \n",
    "        self.weights = torch.zeros(num_features, 1, \n",
    "                                   dtype=torch.float32,\n",
    "                                   device=device,\n",
    "                                   requires_grad=True) # req. for autograd!\n",
    "        self.bias = torch.zeros(1, \n",
    "                                dtype=torch.float32,\n",
    "                                device=device,\n",
    "                                requires_grad=True) # req. for autograd!\n",
    "\n",
    "    def forward(self, x):\n",
    "        linear = torch.add(torch.mm(x, self.weights), self.bias)\n",
    "        probas = self._sigmoid(linear)\n",
    "        return probas\n",
    "                    \n",
    "    def predict_labels(self, x):\n",
    "        probas = self.forward(x)\n",
    "        labels = custom_where((probas >= .5).float(), 1, 0)\n",
    "        return labels    \n",
    "            \n",
    "    def evaluate(self, x, y):\n",
    "        labels = self.predict_labels(x)\n",
    "        accuracy = (torch.sum(labels.view(-1) == y.view(-1))).float() / y.size()[0]\n",
    "        return accuracy\n",
    "    \n",
    "    def _sigmoid(self, z):\n",
    "        return 1. / (1. + torch.exp(-z))\n",
    "    \n",
    "    def _logit_cost(self, y, proba):\n",
    "        tmp1 = torch.mm(-y.view(1, -1), torch.log(proba))\n",
    "        tmp2 = torch.mm((1 - y).view(1, -1), torch.log(1 - proba))\n",
    "        return tmp1 - tmp2\n",
    "    \n",
    "    def train(self, x, y, num_epochs, learning_rate=0.01):\n",
    "        \n",
    "        for e in range(num_epochs):\n",
    "            \n",
    "            #### Compute outputs ####\n",
    "            proba = self.forward(x)\n",
    "            cost = self._logit_cost(y, proba)\n",
    "            \n",
    "            #### Compute gradients ####\n",
    "            cost.backward()\n",
    "            \n",
    "            #### Update weights ####\n",
    "            \n",
    "            tmp = self.weights.detach()\n",
    "            tmp -= learning_rate * self.weights.grad\n",
    "            \n",
    "            tmp = self.bias.detach()\n",
    "            tmp -= learning_rate * self.bias.grad\n",
    "            \n",
    "            #### Reset gradients to zero for next iteration ####\n",
    "            self.weights.grad.zero_()\n",
    "            self.bias.grad.zero_()\n",
    "    \n",
    "            #### Logging ####\n",
    "            print('Epoch: %03d' % (e+1), end=\"\")\n",
    "            print(' | Train ACC: %.3f' % self.evaluate(x, y), end=\"\")\n",
    "            print(' | Cost: %.3f' % self._logit_cost(y, self.forward(x)))\n",
    "            \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 001 | Train ACC: 0.987 | Cost: 5.581\n",
      "Epoch: 002 | Train ACC: 0.987 | Cost: 4.882\n",
      "Epoch: 003 | Train ACC: 1.000 | Cost: 4.381\n",
      "Epoch: 004 | Train ACC: 1.000 | Cost: 3.998\n",
      "Epoch: 005 | Train ACC: 1.000 | Cost: 3.693\n",
      "Epoch: 006 | Train ACC: 1.000 | Cost: 3.443\n",
      "Epoch: 007 | Train ACC: 1.000 | Cost: 3.232\n",
      "Epoch: 008 | Train ACC: 1.000 | Cost: 3.052\n",
      "Epoch: 009 | Train ACC: 1.000 | Cost: 2.896\n",
      "Epoch: 010 | Train ACC: 1.000 | Cost: 2.758\n",
      "\n",
      "Model parameters:\n",
      "  Weights: tensor([[ 4.2267],\n",
      "        [-2.9613]], device='cuda:0', requires_grad=True)\n",
      "  Bias: tensor([0.0994], device='cuda:0', requires_grad=True)\n"
     ]
    }
   ],
   "source": [
    "X_train_tensor = torch.tensor(X_train, dtype=torch.float32, device=device)\n",
    "y_train_tensor = torch.tensor(y_train, dtype=torch.float32, device=device)\n",
    "\n",
    "logr = LogisticRegression2(num_features=2)\n",
    "logr.train(X_train_tensor, y_train_tensor, num_epochs=10, learning_rate=0.1)\n",
    "\n",
    "print('\\nModel parameters:')\n",
    "print('  Weights: %s' % logr.weights)\n",
    "print('  Bias: %s' % logr.bias)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Evaluating the Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test set accuracy: 100.00%\n"
     ]
    }
   ],
   "source": [
    "X_test_tensor = torch.tensor(X_test, dtype=torch.float32, device=device)\n",
    "y_test_tensor = torch.tensor(y_test, dtype=torch.float32, device=device)\n",
    "\n",
    "test_acc = logr.evaluate(X_test_tensor, y_test_tensor)\n",
    "print('Test set accuracy: %.2f%%' % (test_acc*100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "##########################\n",
    "### 2D Decision Boundary\n",
    "##########################\n",
    "\n",
    "w, b = logr.weights, logr.bias\n",
    "\n",
    "x_min = -2\n",
    "y_min = ( (-(w[0] * x_min) - b[0]) \n",
    "          / w[1] )\n",
    "\n",
    "x_max = 2\n",
    "y_max = ( (-(w[0] * x_max) - b[0]) \n",
    "          / w[1] )\n",
    "\n",
    "\n",
    "fig, ax = plt.subplots(1, 2, sharex=True, figsize=(7, 3))\n",
    "\n",
    "ax[0].plot([x_min, x_max], [y_min, y_max])\n",
    "ax[1].plot([x_min, x_max], [y_min, y_max])\n",
    "\n",
    "ax[0].scatter(X_train[y_train==0, 0], X_train[y_train==0, 1], label='class 0', marker='o')\n",
    "ax[0].scatter(X_train[y_train==1, 0], X_train[y_train==1, 1], label='class 1', marker='s')\n",
    "\n",
    "ax[1].scatter(X_test[y_test==0, 0], X_test[y_test==0, 1], label='class 0', marker='o')\n",
    "ax[1].scatter(X_test[y_test==1, 0], X_test[y_test==1, 1], label='class 1', marker='s')\n",
    "\n",
    "ax[1].legend(loc='upper left')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## High-level implementation using the nn.Module API"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "class LogisticRegression3(torch.nn.Module):\n",
    "\n",
    "    def __init__(self, num_features):\n",
    "        super(LogisticRegression3, self).__init__()\n",
    "        self.linear = torch.nn.Linear(num_features, 1)\n",
    "        # initialize weights to zeros here,\n",
    "        # since we used zero weights in the\n",
    "        # manual approach\n",
    "        \n",
    "        self.linear.weight.detach().zero_()\n",
    "        self.linear.bias.detach().zero_()\n",
    "        # Note: the trailing underscore\n",
    "        # means \"in-place operation\" in the context\n",
    "        # of PyTorch\n",
    "        \n",
    "    def forward(self, x):\n",
    "        logits = self.linear(x)\n",
    "        probas = torch.sigmoid(logits)\n",
    "        return probas\n",
    "\n",
    "model = LogisticRegression3(num_features=2).to(device)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "##### Define cost function and set up optimizer #####\n",
    "cost_fn = torch.nn.BCELoss(reduction='sum')\n",
    "# average_size=False to match results in\n",
    "# manual approach, where we did not normalize\n",
    "# the cost by the batch size\n",
    "optimizer = torch.optim.SGD(model.parameters(), lr=0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 001 | Train ACC: 0.987 | Cost: 5.581\n",
      "Epoch: 002 | Train ACC: 0.987 | Cost: 4.882\n",
      "Epoch: 003 | Train ACC: 1.000 | Cost: 4.381\n",
      "Epoch: 004 | Train ACC: 1.000 | Cost: 3.998\n",
      "Epoch: 005 | Train ACC: 1.000 | Cost: 3.693\n",
      "Epoch: 006 | Train ACC: 1.000 | Cost: 3.443\n",
      "Epoch: 007 | Train ACC: 1.000 | Cost: 3.232\n",
      "Epoch: 008 | Train ACC: 1.000 | Cost: 3.052\n",
      "Epoch: 009 | Train ACC: 1.000 | Cost: 2.896\n",
      "Epoch: 010 | Train ACC: 1.000 | Cost: 2.758\n",
      "\n",
      "Model parameters:\n",
      "  Weights: Parameter containing:\n",
      "tensor([[ 4.2267, -2.9613]], device='cuda:0', requires_grad=True)\n",
      "  Bias: Parameter containing:\n",
      "tensor([0.0994], device='cuda:0', requires_grad=True)\n"
     ]
    }
   ],
   "source": [
    "def comp_accuracy(label_var, pred_probas):\n",
    "    pred_labels = custom_where((pred_probas > 0.5).float(), 1, 0).view(-1)\n",
    "    acc = torch.sum(pred_labels == label_var.view(-1)).float() / label_var.size(0)\n",
    "    return acc\n",
    "\n",
    "\n",
    "num_epochs = 10\n",
    "\n",
    "X_train_tensor = torch.tensor(X_train, dtype=torch.float32, device=device)\n",
    "y_train_tensor = torch.tensor(y_train, dtype=torch.float32, device=device).view(-1, 1)\n",
    "\n",
    "\n",
    "for epoch in range(num_epochs):\n",
    "    \n",
    "    #### Compute outputs ####\n",
    "    out = model(X_train_tensor)\n",
    "    \n",
    "    #### Compute gradients ####\n",
    "    cost = cost_fn(out, y_train_tensor)\n",
    "    optimizer.zero_grad()\n",
    "    cost.backward()\n",
    "    \n",
    "    #### Update weights ####  \n",
    "    optimizer.step()\n",
    "    \n",
    "    #### Logging ####      \n",
    "    pred_probas = model(X_train_tensor)\n",
    "    acc = comp_accuracy(y_train_tensor, pred_probas)\n",
    "    print('Epoch: %03d' % (epoch + 1), end=\"\")\n",
    "    print(' | Train ACC: %.3f' % acc, end=\"\")\n",
    "    print(' | Cost: %.3f' % cost_fn(pred_probas, y_train_tensor))\n",
    "\n",
    "\n",
    "    \n",
    "print('\\nModel parameters:')\n",
    "print('  Weights: %s' % model.linear.weight)\n",
    "print('  Bias: %s' % model.linear.bias)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Evaluating the Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test set accuracy: 100.00%\n"
     ]
    }
   ],
   "source": [
    "X_test_tensor = torch.tensor(X_test, dtype=torch.float32, device=device)\n",
    "y_test_tensor = torch.tensor(y_test, dtype=torch.float32, device=device)\n",
    "\n",
    "pred_probas = model(X_test_tensor)\n",
    "test_acc = comp_accuracy(y_test_tensor, pred_probas)\n",
    "\n",
    "print('Test set accuracy: %.2f%%' % (test_acc*100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "##########################\n",
    "### 2D Decision Boundary\n",
    "##########################\n",
    "\n",
    "w, b = logr.weights, logr.bias\n",
    "\n",
    "x_min = -2\n",
    "y_min = ( (-(w[0] * x_min) - b[0]) \n",
    "          / w[1] )\n",
    "\n",
    "x_max = 2\n",
    "y_max = ( (-(w[0] * x_max) - b[0]) \n",
    "          / w[1] )\n",
    "\n",
    "\n",
    "fig, ax = plt.subplots(1, 2, sharex=True, figsize=(7, 3))\n",
    "ax[0].plot([x_min, x_max], [y_min, y_max])\n",
    "ax[1].plot([x_min, x_max], [y_min, y_max])\n",
    "\n",
    "ax[0].scatter(X_train[y_train==0, 0], X_train[y_train==0, 1], label='class 0', marker='o')\n",
    "ax[0].scatter(X_train[y_train==1, 0], X_train[y_train==1, 1], label='class 1', marker='s')\n",
    "\n",
    "ax[1].scatter(X_test[y_test==0, 0], X_test[y_test==0, 1], label='class 0', marker='o')\n",
    "ax[1].scatter(X_test[y_test==1, 0], X_test[y_test==1, 1], label='class 1', marker='s')\n",
    "\n",
    "ax[1].legend(loc='upper left')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "matplotlib 3.0.2\n",
      "numpy      1.15.4\n",
      "torch      1.0.0\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%watermark -iv"
   ]
  }
 ],
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