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{
"cells": [
{
"cell_type": "markdown",
"id": "e22794c1",
"metadata": {},
"source": [
"# Multi-parametric OLS\n",
"The multiprarmetric linear regression is a training procedure based on a linear model. The model makes a prediction by simply computing a weighted sum of the input features, plus a constant term called the bias term (also called the intercept term):\n",
"\n",
"$$ \\hat{y}=\\theta_0 + \\theta_1 x_1 + \\theta_2 x_2 + \\cdots + \\theta_n x_n$$\n",
"\n",
"This new model includes $\\theta_n$ unknown parameter. Thus, the model can be writen more easy by using vector notation form for $m$ instances. \n",
"Therefore, the model will become in matrix form $Y=X\\times\\theta$:\n",
"\n",
"$$ \n",
"\\begin{bmatrix} \n",
" \\hat{y}^0 \\\\ \n",
" \\hat{y}^1\\\\ \n",
" \\hat{y}^2\\\\ \n",
" \\vdots \\\\ \n",
" \\hat{y}^m \n",
"\\end{bmatrix} \n",
"= \n",
"\\begin{bmatrix} \n",
" 1 & x_1^0 & x_2^0 & \\cdots & x_n^0\\\\ \n",
" 1 & x_1^1 & x_2^1 & \\cdots & x_n^1\\\\\n",
" 1 & x_1^2 & x_2^2 & \\cdots & x_n^2\\\\\n",
" \\vdots & \\vdots & \\vdots &\\cdots& \\vdots\\\\\n",
" 1 & x_0^m & x_1^m & \\cdots &x_n^m \n",
"\\end{bmatrix} \n",
"\\begin{bmatrix} \n",
" \\theta_0 \\\\ \n",
" \\theta_1 \\\\ \n",
" \\theta_2 \\\\ \n",
" \\vdots \\\\ \n",
" \\theta_n \n",
"\\end{bmatrix} $$ \n",
"Resulting:\n",
"\n",
"$$\\hat{y}= h_\\theta(x) = x \\theta $$\n",
"\n",
"Now that we have our model, how do we train it?\n",
"\n",
"Please, consider that training the model means adjusting the parameters to reduce the error or minimizing the cost function. \n",
"The most common performance measure of a regression model is the Mean Square Error (MSE). Therefore, to train a Linear Regression model, you need to find the value of $\\theta$ that minimizes the MSE:\n",
"\n",
"$$J = MSE(X,h_\\theta) = \\frac{1}{m} \\sum_{i=1}^{m} \\left(\\hat{y}^{(i)}-y^{(i)} \\right)^2$$\n",
"\n",
"$$J = MSE(X,h_\\theta) = \\frac{1}{m} \\sum_{i=1}^{m} \\left( x^{(i)}\\theta-y^{(i)} \\right)^2$$\n",
"\n",
"$$J = MSE(X,h_\\theta) = \\frac{1}{m} \\left( x\\theta-y \\right)^T \\left( x\\theta-y \\right)$$"
]
},
{
"cell_type": "markdown",
"id": "a9bb4e9b",
"metadata": {},
"source": [
"# The normal equation\n",
"\n",
"To find the value of $\\theta$ that minimizes the cost function, there is a closed-form solution that gives the result directly. \n",
"This is called the Normal Equation; and can be find it by derivating the MSE equation as a function of $\\theta$ and making it equals to zero:\n",
"\n",
"$$\\hat{\\theta} = (X^T X)^{-1} X^{T} y $$"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "6bbfeb7d",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>X1</th>\n",
" <th>X2</th>\n",
" <th>y</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>3.745401</td>\n",
" <td>0.314292</td>\n",
" <td>9.247570</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>9.507143</td>\n",
" <td>6.364104</td>\n",
" <td>16.257728</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>7.319939</td>\n",
" <td>3.143560</td>\n",
" <td>16.258844</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>5.986585</td>\n",
" <td>5.085707</td>\n",
" <td>6.359638</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>1.560186</td>\n",
" <td>9.075665</td>\n",
" <td>-9.739221</td>\n",
" </tr>\n",
" <tr>\n",
" <th>...</th>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" </tr>\n",
" <tr>\n",
" <th>95</th>\n",
" <td>4.937956</td>\n",
" <td>3.492096</td>\n",
" <td>6.523018</td>\n",
" </tr>\n",
" <tr>\n",
" <th>96</th>\n",
" <td>5.227328</td>\n",
" <td>7.259557</td>\n",
" <td>28.761328</td>\n",
" </tr>\n",
" <tr>\n",
" <th>97</th>\n",
" <td>4.275410</td>\n",
" <td>8.971103</td>\n",
" <td>-4.306011</td>\n",
" </tr>\n",
" <tr>\n",
" <th>98</th>\n",
" <td>0.254191</td>\n",
" <td>8.870864</td>\n",
" <td>-19.500923</td>\n",
" </tr>\n",
" <tr>\n",
" <th>99</th>\n",
" <td>1.078914</td>\n",
" <td>7.798755</td>\n",
" <td>-10.525044</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>100 rows × 3 columns</p>\n",
"</div>"
],
"text/plain": [
" X1 X2 y\n",
"0 3.745401 0.314292 9.247570\n",
"1 9.507143 6.364104 16.257728\n",
"2 7.319939 3.143560 16.258844\n",
"3 5.986585 5.085707 6.359638\n",
"4 1.560186 9.075665 -9.739221\n",
".. ... ... ...\n",
"95 4.937956 3.492096 6.523018\n",
"96 5.227328 7.259557 28.761328\n",
"97 4.275410 8.971103 -4.306011\n",
"98 0.254191 8.870864 -19.500923\n",
"99 1.078914 7.798755 -10.525044\n",
"\n",
"[100 rows x 3 columns]"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import pandas as pd\n",
"df = pd.read_csv('dataset1.csv')\n",
"x1 = df['X1']\n",
"df"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "567f8438",
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pyplot as plt\n",
"x1 = df['X1']\n",
"x2 = df['X2']\n",
"y = df['y']\n",
"plt.plot(x1,y, '.k')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "695dbdbe",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Create figure and 3D axis\n",
"fig = plt.figure()\n",
"ax = fig.add_subplot(111, projection='3d')\n",
"\n",
"# Scatter plot\n",
"ax.scatter(x1, x2, y, c='blue', marker='o')\n",
"ax.view_init(elev=20, azim=60) # adjust camera\n",
"\n",
"# Axis labels\n",
"ax.set_xlabel(\"X1\")\n",
"ax.set_ylabel(\"X2\")\n",
"ax.set_zlabel(\"Y\")\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "92a0e7d7",
"metadata": {},
"source": [
"# The normal equation"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "a5ae94cb",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 0.85319677, 2.98010241, -1.871685 ])"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import numpy as np\n",
"from numpy.linalg import inv \n",
"x0 = np.ones(len(x1)) \n",
"X = np.c_[x0,x1,x2]\n",
"thetaH = np.dot(inv(X.T@X), X.T@y)\n",
"thetaH"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "e31f0319",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x1New = np.linspace(0,10,10)\n",
"x2New= np.linspace(0,10,10)\n",
"x1NewG, x2NewG = np.meshgrid(x1New, x2New)\n",
"yModel = thetaH[0]+thetaH[1]*x1NewG+thetaH[2]*x2NewG\n",
"\n",
"fig = plt.figure()\n",
"ax = fig.add_subplot(111, projection='3d')\n",
"ax.scatter(x1NewG, x2NewG, yModel, c='red', marker='.')\n",
"ax.scatter(x1, x2, y, c='black', marker='.')\n",
"ax.view_init(elev=30, azim=30) # adjust camera\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "6b375645",
"metadata": {},
"source": [
"# Batch Gradient Descent\n",
"\n",
"$$\\theta_{new} = \\theta_{old}-\\eta \\nabla_\\theta$$\n",
"$$\\nabla_\\theta = \\frac{2}{m}X^T(X\\theta-y)$$"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "604264ba",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(x1,y, '.k', label=\"data\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "544f3777",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[10],\n",
" [ 9]])"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#bgd:\n",
"X = np.c_[np.ones_like(x1), x1]\n",
"y = np.array(y, ndmin=2).reshape(-1,1)\n",
"np.random.seed(67)\n",
"n = 1000\n",
"m = len(y)\n",
"eta = 0.0001\n",
"thetaH = np.array([[10],[9]])\n",
"thetaH"
]
},
{
"cell_type": "code",
"execution_count": 29,
"id": "a512e89d",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"-=-=-=-=-=-=\n",
"[[9.99064619]\n",
" [8.94558151]]\n",
"-=-=-=-=-=-=\n",
"[[9.2750177 ]\n",
" [4.93169627]]\n",
"-=-=-=-=-=-=\n",
"[[8.85060396]\n",
" [2.80897556]]\n",
"-=-=-=-=-=-=\n",
"[[8.58094375]\n",
" [1.68958788]]\n",
"-=-=-=-=-=-=\n",
"[[8.39363522]\n",
" [1.10248799]]\n",
"-=-=-=-=-=-=\n",
"[[8.25026369]\n",
" [0.79775963]]\n",
"-=-=-=-=-=-=\n",
"[[8.13044659]\n",
" [0.64280814]]\n",
"-=-=-=-=-=-=\n",
"[[8.02336849]\n",
" [0.56728464]]\n",
"-=-=-=-=-=-=\n",
"[[7.92328982]\n",
" [0.53386527]]\n",
"-=-=-=-=-=-=\n",
"[[7.82716409]\n",
" [0.52274774]]\n",
"Final values:\n",
"[[7.73430322]\n",
" [0.52338189]]\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"thetaH = np.array([[10],[9]])\n",
"x1New = np.linspace(0,10,2)\n",
"plt.scatter(x1, y, color=\"k\", s=15, label=\"data\")\n",
"#yModel = thetaH[0]+thetaH[1]*x1New\n",
"#plt.plot(x1New, yModel, '-g', label=\"zero\")\n",
"for iter in range(n):\n",
" nabla = 2/m * X.T@(X@thetaH-y)\n",
" thetaH = thetaH-eta*nabla\n",
" if iter % 100 == 0:\n",
" yModel = thetaH[0]+thetaH[1]*x1New\n",
" plt.plot(x1New,yModel, label=f\"iter {iter}\")\n",
" print(\"-=-=-=-=-=-=\")\n",
" print(thetaH)\n",
"print(\"Final values:\")\n",
"print(thetaH) \n",
"plt.xlabel(\"x1\")\n",
"plt.ylabel(\"y\")\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "b1bbdec0",
"metadata": {},
"source": [
"# History"
]
},
{
"cell_type": "code",
"execution_count": 99,
"id": "a8a864bc",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Initial values\n",
"[[ 0.47298583]\n",
" [-0.68142588]]\n",
"Final values:\n",
"[[-3.25986811]\n",
" [ 2.19754312]]\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"np.random.seed(12)\n",
"thetaH = np.random.randn(2,1)\n",
"print(\"Initial values\")\n",
"print(thetaH)\n",
"thetas = np.zeros((n,2))\n",
"J_hist = np.zeros((n,1))\n",
"thetas[0] = thetaH.ravel()\n",
"x1New = np.linspace(0,10,2)\n",
"plt.scatter(x1, y, color=\"k\", s=15, label=\"data\")\n",
"for iter in range(n):\n",
" nabla = 2/m * X.T@(X@thetaH-y)\n",
" thetaH = thetaH-eta*nabla\n",
" thetas[iter] = thetaH.ravel()\n",
" J = (1/m*(X@thetaH - y).T@(X@thetaH - y))\n",
" # print(\"J init\")\n",
" # print(J)\n",
" J_hist[iter] = J\n",
" if iter % 100 == 0:\n",
" yModel = thetaH[0]+thetaH[1]*x1New\n",
" plt.plot(x1New,yModel, label=f\"iter {iter}\")\n",
" # print(\"-=-=-=-=-=-=\")\n",
" # print(thetaH)\n",
"print(\"Final values:\")\n",
"print(thetaH) \n",
"plt.xlabel(\"x1\")\n",
"plt.ylabel(\"y\")\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 100,
"id": "ad27ce36",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<function matplotlib.pyplot.show(close=None, block=None)>"
]
},
"execution_count": 100,
"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(J_hist,'.r')\n",
"plt.show"
]
},
{
"cell_type": "code",
"execution_count": 107,
"id": "49be25e1",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(thetas[:,0], '.b', label=r\"$\\theta_0$\")\n",
"plt.plot(thetas[:,1], '.r', label=r\"$\\theta_1$\")\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "543bbf87",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(thetas[:,0], thetas[:,1], '.k')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 115,
"id": "5a62a2bc",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(1000, 1)"
]
},
"execution_count": 115,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"J_hist.shape"
]
},
{
"cell_type": "code",
"execution_count": 116,
"id": "502253bf",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure()\n",
"ax = fig.add_subplot(111, projection='3d')\n",
"ax.scatter(thetas[:,0], thetas[:,1], J_hist[:,0], c='red', marker='.')\n",
"ax.view_init(elev=30, azim=30) # adjust camera\n",
"plt.show()"
]
}
],
"metadata": {
"kernelspec": {
"display_name": ".venv (3.13.5)",
"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": "3.13.5"
}
},
"nbformat": 4,
"nbformat_minor": 5
}