Linear-Regression/Using-torch-operations.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "eae54ff5",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "from torch.utils.data import DataLoader, TensorDataset\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22326d97",
   "metadata": {},
   "source": [
    "# Toy dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "f1016e10",
   "metadata": {},
   "outputs": [],
   "source": [
    "Train_X = torch.arange(10).to(torch.float32).reshape(10,1)\n",
    "Train_X_Norm = (Train_X - Train_X.mean())/ Train_X.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "3d63ffc2",
   "metadata": {},
   "outputs": [],
   "source": [
    "Train_Y = torch.tensor([1.0, 1.3, 3.1, 2.0, 5.0, 6.3, 6.6, 7.4, 8.0, 9.0])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66844b77",
   "metadata": {},
   "source": [
    "# Visualize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "cdbd9d29",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '$y$')"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(Train_X_Norm, \n",
    "         Train_Y,\n",
    "         linestyle=\"\",\n",
    "         marker=\"D\")\n",
    "plt.xlabel(\"$x$\", size=18)\n",
    "plt.ylabel(\"$y$\", size=18)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "865fa6ad",
   "metadata": {},
   "source": [
    "# Initialize Dataloader iterator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "58045ec8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([-1.4863]), tensor(1.))"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "toy_data = TensorDataset(Train_X_Norm, Train_Y)\n",
    "toy_data[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "5e25e07d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[tensor([[-1.4863]]), tensor([1.])]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = DataLoader(toy_data, batch_size=1)\n",
    "next(iter(data))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0b5bcd57",
   "metadata": {},
   "source": [
    "# Initialize trainable parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "a786595f",
   "metadata": {},
   "outputs": [],
   "source": [
    "weights = torch.rand(1, requires_grad=True)\n",
    "bias = torch.rand(1, requires_grad=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2eb55b30",
   "metadata": {},
   "source": [
    "# Model "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "aaf1d9ef",
   "metadata": {},
   "outputs": [],
   "source": [
    "def model(x):\n",
    "    return x @ weights + bias"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ebb1e2cd",
   "metadata": {},
   "source": [
    "# Loss Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "a1abd605",
   "metadata": {},
   "outputs": [],
   "source": [
    "def loss_func(prediction, label):\n",
    "    return ((prediction - label).pow(2)).mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "037374be",
   "metadata": {},
   "source": [
    "# Train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "783e53de",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 1, Error: 80.21822357177734\n",
      "Epoch: 11, Error: 54.029178619384766\n",
      "Epoch: 21, Error: 36.31801986694336\n",
      "Epoch: 31, Error: 24.352272033691406\n",
      "Epoch: 41, Error: 16.278453826904297\n",
      "Epoch: 51, Error: 10.839491844177246\n",
      "Epoch: 61, Error: 7.182991981506348\n",
      "Epoch: 71, Error: 4.731164932250977\n",
      "Epoch: 81, Error: 3.0925004482269287\n",
      "Epoch: 91, Error: 2.001868724822998\n",
      "Epoch: 101, Error: 1.2798612117767334\n",
      "Epoch: 111, Error: 0.8051828145980835\n",
      "Epoch: 121, Error: 0.49592018127441406\n",
      "Epoch: 131, Error: 0.2968473434448242\n",
      "Epoch: 141, Error: 0.17080076038837433\n",
      "Epoch: 151, Error: 0.09282924234867096\n",
      "Epoch: 161, Error: 0.046232447028160095\n",
      "Epoch: 171, Error: 0.019876370206475258\n",
      "Epoch: 181, Error: 0.006375596858561039\n",
      "Epoch: 191, Error: 0.0008618868887424469\n"
     ]
    }
   ],
   "source": [
    "learning_rate = 0.001\n",
    "epoch = 200\n",
    "for i in range(epoch):\n",
    "    for x, y in data:\n",
    "        pred = model(x)\n",
    "        loss = loss_func(pred, y)\n",
    "        loss.backward()\n",
    "    with torch.no_grad():\n",
    "        weights -= weights.grad * learning_rate\n",
    "        bias -= bias.grad * learning_rate\n",
    "        weights.grad.zero_()\n",
    "        bias.grad.zero_()\n",
    "    if (i % 10 == 0):\n",
    "        print(f\"Epoch: {i+1}, Error: {loss}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80befe67",
   "metadata": {},
   "source": [
    "# To visualize regression line"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "4e8c91c4",
   "metadata": {},
   "outputs": [],
   "source": [
    "prediction = model(Train_X_Norm).detach()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "ffd8fc92",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x126d8cc10>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(Train_X_Norm,\n",
    "         Train_Y,\n",
    "         linestyle=\"\",\n",
    "         marker=\"D\")\n",
    "\n",
    "plt.plot(Train_X_Norm,\n",
    "         prediction,\n",
    "         linestyle=\"--\")\n",
    "\n",
    "\n",
    "plt.xlabel(\"$x$\", size=18)\n",
    "plt.ylabel(\"$y$\", size=18)\n",
    "\n",
    "plt.legend(['Training Example', 'Prediction'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fe1eeaf0",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.9 (pytorch)",
   "language": "python",
   "name": "pytorch"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}