Lineer_regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "2ee598a5",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy  as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from sklearn.preprocessing import LabelEncoder"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "97b33b89",
   "metadata": {},
   "source": [
    "In this notebook we will look at linear regression using gradient descent. We will generate synthetic data and try our algorithm on it. First we will generate a perfect line and then add some gaussian noise on it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "82593fc0",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(0)\n",
    "a0 = 0.6 \n",
    "a1 = 0.3\n",
    "\n",
    "x = np.arange(0,20,0.1)\n",
    "y = a1 * x + a0 # our perfect line\n",
    "\n",
    "# we are adding random gaussian noise to our data  \n",
    "y = y + np.random.normal(0,0.5,y.shape[0])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "2ffc6bca",
   "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,y)\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "42781291",
   "metadata": {},
   "source": [
    "Since we have a single feature we will have two coefficients. Our predictions will be in the form of y = wx +b.\n",
    "We use mean squared error to calculate our error. In gradient descent algorithm we calculate our error, calculate the gradient and then go in the direction along the gradient since we want to minimize our error. To be able to do this we need to calculate the gradient by hand. Our error is (y_pred - y_real)^2 also we can write it as (wx+b - y_real)^2. If you take the derivate for w you will find that the derivate is (y_pred - y_real) * x * 2. For b the derivative is (y_pred - y) * 2. We initialize our coefficients randomly and iteratively update using the gradient which will get us to the solution. Note that the best approach is to plot the loss and cut the training on a low loss value before it starts overfitting. However we skip this step since we just want to see our implementation working."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "10fbed7e",
   "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"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients w:[0.29491485] , b: [0.68714639]\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(0)\n",
    "w = np.random.rand(1)\n",
    "b = np.random.rand(1)\n",
    "\n",
    "lr = 10**-5 # we set the learning rate \n",
    "epoch = 1200 # we set how many times we will go over the data\n",
    "\n",
    "for _ in range(epoch):\n",
    "    for i,j in zip(x,y):\n",
    "        pred = w * i + b\n",
    "        w-= lr * (pred - j) * i * 2\n",
    "        b-= lr * (pred - j) * 2\n",
    "\n",
    "plt.scatter(x,w*x+b) # predictions\n",
    "plt.scatter(x,y) # real data\n",
    "plt.grid()\n",
    "plt.show()       \n",
    "print(\"Coefficients w:{} , b: {}\".format(w,b))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb570859",
   "metadata": {},
   "source": [
    "We will also try sci-kit learns linear regression implementation and compare the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "16a2f8ed",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "lr = LinearRegression()\n",
    "lr.fit(x.reshape(-1,1),y)\n",
    "y_sklearn = lr.predict(x.reshape(-1,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "6b013efa",
   "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"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients w:[0.29530664] , b: 0.6821541524654005\n"
     ]
    }
   ],
   "source": [
    "plt.scatter(x,y_sklearn)\n",
    "plt.scatter(x,y)\n",
    "plt.grid()\n",
    "plt.show()\n",
    "print(\"Coefficients w:{} , b: {}\".format(lr.coef_,lr.intercept_))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d267d99",
   "metadata": {},
   "source": [
    "As you can see we get similar results with the sci-kit's implementation. Our coefficients are really close to what sci-kit's linear regressor found. You can see this better in the plot below. Lines predicted by both implementations are so close they one of them block the other on the plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "05282a2b",
   "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,w*x+b) # scratch model predics similar to sklearn\n",
    "plt.scatter(x,y_sklearn)\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "94d6da8d",
   "metadata": {},
   "source": [
    "Lastly we will implement the closed form solution. In gradient descent we calculate gradients at each step using our error and slowly move in the direction of the gradient with the goal of making the error zero. However we can actually do this in a single step. We can do this by calculating the gradient, setting to zero and solving the equation. Note that now the input x will not be a single sample but the whole dataset. The equation will now be in the form of Y = X * B. Here B is our coefficients or in other terms (w,b). X is the whole dataset and because we are using matrix multiplications X will have a second column of ones. So X will be in the form of ((x1,1),(x2,1),.....(xn,1)). Lets check the multiplication just for the first row. (x1,1) * (w,b) = x1 * w + 1 * b = wx+b. So we add the ones column just to use matrix operations. If you do the calculations you will find that the value of B matrix which gives us the lowest loss is equal to (X.T * X)-1 * X.T * y . Here T denotes transpose of the matrix, -1 is the inverse of the matrix and * is the dot product. If we compute this it will should give us the same regression coefficients as before."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "3ad12a15",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.stack((x,np.ones(x.shape[0])),axis=1) # add column of ones\n",
    "\n",
    "# we break the operations into a couple of steps to make it more clear\n",
    "c0 = np.dot(X.T,X)\n",
    "c1 = np.linalg.inv(c0)\n",
    "c2 = np.dot(c1,X.T)\n",
    "c3 = np.dot(c2,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "0d892ecb",
   "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"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients w:0.29530664262363604 , b: 0.6821541524654031\n"
     ]
    }
   ],
   "source": [
    "y_closed = np.dot(X,c3)\n",
    "\n",
    "plt.scatter(x,y_closed)\n",
    "plt.scatter(x,y)\n",
    "plt.grid()\n",
    "plt.show()   \n",
    "print(\"Coefficients w:{} , b: {}\".format(c3[0],c3[1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2f7b9d3b",
   "metadata": {},
   "source": [
    "Now lets compare the cofficients we have found using each method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "2439bcd8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients of gradient descent w:0.2949 , b: 0.6871\n",
      "Coefficients of scikit w:0.2953 , b: 0.6822\n",
      "Coefficients closed form solution w:0.2953 , b: 0.6822\n"
     ]
    }
   ],
   "source": [
    "print(\"Coefficients of gradient descent w:{:.4f} , b: {:.4f}\".format(w[0],b[0]))\n",
    "print(\"Coefficients of scikit w:{:.4f} , b: {:.4f}\".format(lr.coef_[0],lr.intercept_))\n",
    "print(\"Coefficients closed form solution w:{:.4f} , b: {:.4f}\".format(c3[0],c3[1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "003e8174",
   "metadata": {},
   "source": [
    "You can see that more or less we find the same results in each solution. After seeing the closed form solution you may think why we bother with the gradient descent anyway, the problem is as your data gets bigger you matrix size X and Y gets bigger. This results in more matrix operations and don't forget that you have to compute mutliple matrix operations such as getting the transpose, taking the inverse and dot product. So which way to go depends on the efficieny for a particular situation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0e62d449",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "59725a2d",
   "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": "3.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}