04_logistic_regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(6)\n",
    "torch.manual_seed(0)\n",
    "x0 = np.random.randn(100,2) * 0.2 + np.array([2,2])\n",
    "x1 = np.random.randn(100,2) * 0.2 + np.array([3,1])\n",
    "x2 = np.random.rand(5,2)*1.5 + np.array([2,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fc347d009a0>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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(x0[:,0], x0[:,1], c='c', label='label: 0')\n",
    "plt.scatter(x1[:,0], x1[:,1], c='y', label='label: 1')\n",
    "plt.scatter(x2[:,0], x2[:,1], c='k', label='label: ?')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.concatenate([x0, x1])\n",
    "y = np.array([0]*100 + [1]*100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sigmoid function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\text{sigmoid}(x) = \\frac{1}{1+e^{-x}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(x):\n",
    "    return 1/(1+torch.exp(-x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Logistic Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "H(X) = \\text{sigmoid}(\\,\\mathbf{XW} +\\mathbf{b})\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Binary Cross Entropy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ cost(W) = -\\frac{1}{m} \\sum y \\log\\left(H(x)\\right) + (1-y) \\left( \\log(1-H(x) \\right) $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def binary_cross_entropy(y_pred, y):\n",
    "    return -torch.mean(y * torch.log(y_pred) + (1-y) * torch.log(1-y_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implimentation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def LogisticRegression(X):\n",
    "    return sigmoid(X @ W + b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch:10   loss:0.682   acc:0.750\n",
      "epoch:20   loss:0.671   acc:0.810\n",
      "epoch:30   loss:0.660   acc:0.855\n",
      "epoch:40   loss:0.650   acc:0.920\n",
      "epoch:50   loss:0.639   acc:0.945\n",
      "epoch:60   loss:0.629   acc:0.980\n",
      "epoch:70   loss:0.620   acc:0.990\n",
      "epoch:80   loss:0.610   acc:0.995\n",
      "epoch:90   loss:0.601   acc:1.000\n",
      "epoch:100   loss:0.592   acc:1.000\n"
     ]
    }
   ],
   "source": [
    "X_train = torch.Tensor(X)\n",
    "y_train = torch.Tensor(y).unsqueeze(1)\n",
    "X_test = torch.Tensor(x2)\n",
    "\n",
    "W = torch.zeros(2, 1, requires_grad=True)\n",
    "b = torch.zeros(1, requires_grad=True)\n",
    "\n",
    "n_epochs = 100\n",
    "lr = 0.01\n",
    "\n",
    "for epoch in range(n_epochs):\n",
    "    \n",
    "    y_pred = LogisticRegression(X_train)\n",
    "    loss = binary_cross_entropy(y_pred, y_train)\n",
    "    loss.backward()\n",
    "    \n",
    "    with torch.no_grad():\n",
    "        \n",
    "        # backward propagation\n",
    "        for param in [W, b]:\n",
    "            param -= lr * param.grad\n",
    "            param.grad.data.zero_()\n",
    "        \n",
    "        # calculate accuracy\n",
    "        acc = torch.sum((y_pred >= 0.5) == y_train).item() / len(X_train) \n",
    "\n",
    "    if (epoch+1)%10 == 0:\n",
    "        print(f'epoch:{epoch+1}   loss:{loss.item():.3f}   acc:{acc:.3f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Get prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "with torch.no_grad():\n",
    "    y_test = (LogisticRegression(X_test) >= 0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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_train[:,0], X_train[:,1], c='grey', alpha =0.15)\n",
    "plt.scatter(X_test[:,0], X_test[:,1], marker='x', c=y_test, cmap='rainbow')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using Pytorch libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch.nn as nn\n",
    "\n",
    "class LogisticRegression(nn.Module):\n",
    "    \n",
    "    def __init__(self):\n",
    "        super(LogisticRegression, self).__init__()\n",
    "        self.layer = nn.Linear(2,1)\n",
    "        self.sigmoid = nn.Sigmoid()\n",
    "        \n",
    "    def forward(self, X):\n",
    "        out = self.sigmoid(self.layer(X))\n",
    "        return out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch:10   loss:0.730   acc:0.255\n",
      "epoch:20   loss:0.672   acc:0.555\n",
      "epoch:30   loss:0.621   acc:0.935\n",
      "epoch:40   loss:0.575   acc:0.990\n",
      "epoch:50   loss:0.535   acc:1.000\n",
      "epoch:60   loss:0.499   acc:1.000\n",
      "epoch:70   loss:0.468   acc:1.000\n",
      "epoch:80   loss:0.439   acc:1.000\n",
      "epoch:90   loss:0.414   acc:1.000\n",
      "epoch:100   loss:0.391   acc:1.000\n"
     ]
    }
   ],
   "source": [
    "from torch.optim import SGD\n",
    "\n",
    "X_train = torch.Tensor(X)\n",
    "y_train = torch.Tensor(y).unsqueeze(1)\n",
    "X_test = torch.Tensor(x2)\n",
    "\n",
    "model = LogisticRegression()\n",
    "optimizer = SGD(model.parameters(), lr=0.05)\n",
    "loss_fn = nn.BCELoss()\n",
    "\n",
    "n_epochs = 100\n",
    "\n",
    "for epoch in range(n_epochs):\n",
    "    y_pred = model(X_train)\n",
    "    loss = loss_fn(y_pred, y_train)\n",
    "    optimizer.zero_grad()\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "\n",
    "    with torch.no_grad():\n",
    "        acc = torch.sum((y_pred >= 0.5) == y_train).item() / len(X_train) \n",
    "\n",
    "    if (epoch+1)%10 == 0:\n",
    "        print(f'epoch:{epoch+1}   loss:{loss.item():.3f}   acc:{acc:.3f}')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "pytorch",
   "language": "python",
   "name": "pytorch"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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