fitting-a-straight-line-on-2d-data-in-pytorch.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fitting a Straight Line on 2D Data in PyTorch\n",
    "\n",
    "The objective here is to fit a straight line on a synthetic 2-dimensional or 2D data. \n",
    "\n",
    "This is known as a **Linear Regression Problem**.\n",
    "\n",
    "*Links for the Medium Blog and the Github Repository are mentioned at the end of this notebook !*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<torch._C.Generator at 0x7fe0380c4070>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Importing the bare necessities...\n",
    "seed_for_reproducibility = 3333\n",
    "import numpy as np\n",
    "np.random.seed(seed_for_reproducibility)\n",
    "import random\n",
    "random.seed(seed_for_reproducibility)\n",
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "import torch\n",
    "torch.manual_seed(seed_for_reproducibility)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "_cell_guid": "b1076dfc-b9ad-4769-8c92-a6c4dae69d19",
    "_uuid": "8f2839f25d086af736a60e9eeb907d3b93b6e0e5"
   },
   "source": [
    "> ## STEP 1: Generating Synthetic 2D data\n",
    "\n",
    "> In order to find a straight line that fits a given data, we first need to generate the data itself. We are going to generate the synthetic data in such a way that the data points roughly lie on a stright line. We are going to do this by using some predefined **m** (slope) and **c** (intercept)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "_cell_guid": "79c7e3d0-c299-4dcb-8224-4455121ee9b0",
    "_uuid": "d629ff2d2480ee46fbb7e2d37f6b5fab8052498a"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "m_synthetic: -0.67\n",
      "c_synthetic: 6\n",
      "\n",
      "Following are the extreme ends of the synthetic data points...\n",
      "x_min, x_max: -2022, 1966\n",
      "y_min, y_max: -1392.3200000000002, 1352.16\n"
     ]
    }
   ],
   "source": [
    "# Defining the range of 'x', the independent variable\n",
    "x_range = [-2000, 2000]\n",
    "\n",
    "# Defining the extent of noise, which would be added to both the dependent as well as the independent variable\n",
    "deviation = 100\n",
    "\n",
    "# For the data points to roughly fall on a staright line, we need to define the slope and the intercept of that line\n",
    "# Let's intoduce some randomness in the slope and intercept selection process\n",
    "m_synthetic = random.randint(-100, 100)/100. # m_synthetic is real number from the set(-1.0, -0.99, -0.98 ...., 0.98, 0.99, 1.0)\n",
    "c_synthetic = random.randint(-10, 10)        # c_synthetic is an integer from the set(-10, -9, -8 ..., 8, 9, 10)\n",
    "\n",
    "print('\\nm_synthetic: {}'.format(m_synthetic))\n",
    "print('c_synthetic: {}'.format(c_synthetic))\n",
    "\n",
    "# Defining the number of data points to be generated\n",
    "num_points = 100\n",
    "\n",
    "# Let's generate the synthetic data points\n",
    "x_list = []\n",
    "y_list = []\n",
    "for _ in range(num_points):\n",
    "    \n",
    "    # Selecting a random integer from the predefined range\n",
    "    x = random.randint(x_range[0] , x_range[1])\n",
    "    \n",
    "    # Calculating the dependent valiable 'y' using the formula of a straight line y = mx + c\n",
    "    y = m_synthetic*x + c_synthetic\n",
    "    \n",
    "    # Randomly choosing the deviation (noise) for both the dependent as well as the independent variable, so that the dataset becomes a little noisy\n",
    "    deviation_x = random.randint(-deviation , deviation)\n",
    "    deviation_y = random.randint(-deviation , deviation)\n",
    "    \n",
    "    # Finally, appending the noisy data points in the respective lists\n",
    "    x_list.append(x + deviation_x)\n",
    "    y_list.append(y + deviation_y)\n",
    "\n",
    "x_min, y_min, x_max, y_max = min(x_list) , min(y_list) , max(x_list) , max(y_list)\n",
    "print('\\nFollowing are the extreme ends of the synthetic data points...')\n",
    "print('x_min, x_max: {}, {}'.format(x_min, x_max))\n",
    "print('y_min, y_max: {}, {}'.format(y_min, y_max))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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": [
    "# Let's now visualize how the synthetic data looks like \n",
    "plt.scatter(x_list, y_list , color = 'cyan')\n",
    "plt.plot((x_min, x_max), (m_synthetic*x_min + c_synthetic, m_synthetic*x_max + c_synthetic), color = 'r')\n",
    "plt.title('Synthetic Data with m = {} and c = {}'.format(m_synthetic, c_synthetic))\n",
    "plt.xlabel(\"Independent Variable 'x'\")\n",
    "plt.ylabel(\"Dependent Variable 'y'\")\n",
    "plt.savefig('synthetic_m_and_c.jpg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our task here, is to find out the equation of a straight line which best fits all the data points !\n",
    "\n",
    "In other words, we have to find the slope and the intercept of a line, which would give us the line that sits at the center of the distribution of the data points.\n",
    "\n",
    "Since this is a Linear Regression Problem, we want to find the value of all the required parameters (slope m and intercept c in our case because the data lies in a 2D space)\n",
    "\n",
    "Had the data been higher-dimensional, we would have to solve for more parameteres."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## STEP 2: Define the model architecture\n",
    "\n",
    "We are going to use PyTorch to solve this Linear Regression Problem.\n",
    "We need a very simple model which takes in a single scalar input and spits out some single scalar output."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Defining the model architecture.\n",
    "class LinearRegressionModel(torch.nn.Module): \n",
    "    def __init__(self): \n",
    "        super(LinearRegressionModel, self).__init__() \n",
    "        self.linear = torch.nn.Linear(1, 1)  # this layer of the model has a single neuron, that takes in one scalar input and gives out one scalar output. \n",
    "  \n",
    "    def forward(self, x): \n",
    "        y_pred = self.linear(x) \n",
    "        return y_pred \n",
    "\n",
    "# Creating the model\n",
    "model = LinearRegressionModel()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LinearRegressionModel(\n",
      "  (linear): Linear(in_features=1, out_features=1, bias=True)\n",
      ")\n"
     ]
    }
   ],
   "source": [
    "# We can print the 'model' to see it's architecture\n",
    "print(model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once, we have created the model, let's check out the paramters that we have in it.\n",
    "\n",
    "There are going to be some learnable parameters in the model, which are randomly initialized at the beginning.\n",
    "\n",
    "This is the how the initial parameters look like at the initial stage..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "name           : linear.weight\n",
      "parameter      : -0.19329047203063965\n",
      "learnable      : True\n",
      "parameter.shape: torch.Size([1, 1])\n",
      "---------------------------------\n",
      "name           : linear.bias\n",
      "parameter      : -0.36674630641937256\n",
      "learnable      : True\n",
      "parameter.shape: torch.Size([1])\n",
      "---------------------------------\n"
     ]
    }
   ],
   "source": [
    "for name, parameter in model.named_parameters():\n",
    "    print('name           : {}'.format(name))\n",
    "    print('parameter      : {}'.format(parameter.item()))\n",
    "    print('learnable      : {}'.format(parameter.requires_grad))\n",
    "    print('parameter.shape: {}'.format(parameter.shape))\n",
    "    print('---------------------------------')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the parameter's initialized values are not at all, near the m_synthetic and c_synthetic values, which have been actually used to synthesize the data points.\n",
    "\n",
    "But as we train the model, these values would approach to the values of m_synthetic and c_synthetic ! \n",
    "\n",
    "We will see this at the end of this notebook."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## STEP 3: Defining a Loss Fucntion and an Optimizer\n",
    "\n",
    "There must be a metric which would let us know how well is our model fitting on the given data. \n",
    "\n",
    "That is exactly what a **Loss Function** does !\n",
    "\n",
    "And PyTorch calculates the derivatives of the loss with respect to all the learnable parameters during the Back-Propagation, which is later used by an **Optimizer** to update all the parameters of the model, improving the model after every epoch.\n",
    "\n",
    "By the way, one **epoch** is when the entire dataset is passed both forward and backward through the Neural Network only once."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Defining the Loss Function\n",
    "# Mean Squared Error is the most common choice of Loss Function for Linear Regression models.\n",
    "criterion = torch.nn.MSELoss()\n",
    "\n",
    "# Defining the Optimizer, which would update all the trainable parameters of the model, making the model learn the data distribution better and hence fit the distribution better.\n",
    "optimizer = torch.optim.Adam(model.parameters(), lr = 0.0005) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# We also need to convert all the data into tensors before we could use them for training our model.\n",
    "data_x = torch.tensor([[x] for x in x_list], dtype = torch.float)\n",
    "data_y = torch.tensor([[y] for y in y_list], dtype = torch.float)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## STEP 4: Training the Model and Plotting the Loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "TRAINING...\n",
      "loss:  290066.9375\n",
      "loss:  233668.875\n",
      "loss:  186075.625\n",
      "loss:  146441.828125\n",
      "loss:  113859.40625\n",
      "loss:  87455.7265625\n",
      "loss:  66397.1875\n",
      "loss:  49895.44140625\n",
      "loss:  37213.265625\n",
      "loss:  27672.890625\n",
      "loss:  20661.083984375\n",
      "loss:  15636.8427734375\n",
      "loss:  12134.056640625\n",
      "loss:  9762.8232421875\n",
      "loss:  8207.25390625\n",
      "loss:  7220.21630859375\n",
      "loss:  6615.59326171875\n",
      "loss:  6258.6826171875\n",
      "loss:  6055.97216796875\n",
      "loss:  5945.3681640625\n",
      "loss:  5887.44677734375\n",
      "loss:  5858.3232421875\n",
      "loss:  5844.21875\n",
      "loss:  5837.568359375\n",
      "loss:  5834.42822265625\n",
      "\n",
      "Compare the learnt parameters with the original ones\n",
      "\n",
      "m_synthetic     VS     m_learnt\n",
      "     -0.67                   -0.6612429618835449\n",
      "\n",
      "c_synthetic     VS     c_learnt\n",
      "     6                   0.3956650197505951\n"
     ]
    },
    {
     "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": [
    "losses = []         # to keep track of the epoch lossese \n",
    "slope_list = []     # to keep track of the slope learnt by the model\n",
    "intercept_list = [] # to keep track of the intercept learnt by the model\n",
    "\n",
    "EPOCHS = 2500\n",
    "print('\\nTRAINING...')\n",
    "for epoch in range(EPOCHS):\n",
    "    # We need to clear the gradients of the optimizer before running the back-propagation in PyTorch\n",
    "    optimizer.zero_grad() \n",
    "    \n",
    "    # Feeding the input data in the model and getting out the predictions\n",
    "    pred_y = model(data_x)\n",
    "\n",
    "    # Calculating the loss using the model's predictions and the real y values\n",
    "    loss = criterion(pred_y, data_y) \n",
    "\n",
    "    # Back-Propagation\n",
    "    loss.backward() \n",
    "    \n",
    "    # Updating all the trainable parameters\n",
    "    optimizer.step()\n",
    "    \n",
    "    # Appending the loss.item() (a scalar value)\n",
    "    losses.append(loss.item())\n",
    "    \n",
    "    # Appending the learnt slope and intercept   \n",
    "    slope_list.append(model.linear.weight.item())\n",
    "    intercept_list.append(model.linear.bias.item())\n",
    "    \n",
    "    # We print out the losses after every 2000 epochs\n",
    "    if (epoch)%100 == 0:\n",
    "        print('loss: ', loss.item())\n",
    "\n",
    "# Let's see what are the learnt parameters after having trained the model for hundreds of epochs\n",
    "m_learnt = model.linear.weight.item()\n",
    "c_learnt = model.linear.bias.item()\n",
    "\n",
    "print('\\nCompare the learnt parameters with the original ones')\n",
    "print('\\nm_synthetic     VS     m_learnt')\n",
    "print('     {}                   {}'.format(m_synthetic, m_learnt))\n",
    "print('\\nc_synthetic     VS     c_learnt')\n",
    "print('     {}                   {}'.format(c_synthetic, c_learnt))\n",
    "\n",
    "# Plotting the epoch losses\n",
    "plt.plot(losses)\n",
    "plt.title('Loss VS Epoch')\n",
    "plt.xlabel('#Epoch')\n",
    "plt.ylabel('Loss')\n",
    "plt.savefig('losses.jpg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see the loss coming down after every epoch. That's always a good sight for a Deep Learning practitioner :D "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## STEP 5: Visualizing the Line Learnt by the Model"
   ]
  },
  {
   "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_list, y_list , color = 'cyan')\n",
    "plt.plot((x_min, x_max), (m_learnt*x_min + c_learnt, m_learnt*x_max + c_learnt), color = 'r')\n",
    "plt.title('Synthetic Data Points, with m = {} and c = {}'.format(round(m_learnt, 2), round(c_learnt, 2)))\n",
    "plt.xlabel(\"Independent Variable 'x'\")\n",
    "plt.ylabel(\"Dependent Variable 'y'\")\n",
    "plt.savefig('learnt_m_and_c.jpg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looks like the model has indeed fit a straight line on the given data distribution !!! "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Slope and Intercept during the training of the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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.plot(slope_list)\n",
    "plt.plot(intercept_list)\n",
    "plt.title('Learnt Values of Slope and Intercept')\n",
    "plt.legend(['slope', 'intercept'])\n",
    "plt.xlabel('#Epochs')\n",
    "plt.ylabel('Learnt Parameteres')\n",
    "plt.savefig('learning_m_and_c.jpg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that during the training phase of the model, the parameters of the model change and they approach to the value for which the overall loss of the model is minimum.\n",
    "\n",
    "This in fact, is the general idea behind any Deep Learning model. It tries to find the best suited parameters for the model, to perform a specific task, which is measured by using a suitable Loss Function for that specific task. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### End.\n",
    "\n",
    "I hope that you understood the basic ideas behind solving a Linear Regression problem using PyTorch.\n",
    "\n",
    "This was a very simple example of solving a linear regression problem in 1 variable or a Univariate Regression problem. But we can even solve Multivariate Regression problems using a similar approach.\n",
    "\n",
    "I hope that you enjoyed this tutorial ! :D\n",
    "\n",
    "Check out the following links-\n",
    "\n",
    "Blog on Medium: https://medium.com/@animesh7pointer/fitting-a-straight-line-on-2d-data-in-pytorch-78d0e3450876\n",
    "\n",
    "Github Repository: https://github.com/n0obcoder/Fitting-a-Straight-Line-on-2D-Data-in-PyTorch"
   ]
  }
 ],
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