File size: 48,436 Bytes
bcf16ee
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "dedefa38",
   "metadata": {},
   "source": [
    "## Machine Learning\n",
    "### Linear regression with least squares\n",
    "In **linear regression**, we assume we can model the data points with a linear function as:\n",
    "<br> $y=w_0+w_1x_1+w_2x_2+....w_{p-1}x_{p-1}$\n",
    "<br>Given data points $(\\boldsymbol{x}_i,y_i)$ we may find the best estimate for parameter vector $\\boldsymbol{w}$ using the **least squares method**:<br>\n",
    "$\\boldsymbol{w}=X^+ \\boldsymbol{y}$\n",
    "<br> where $X^+=(X^TX)^{-1}X^T$, and it it called the **pseudo-inverse** of $X$. \n",
    "<br> **Reminder:** The rows of matrix $X$ are composed of $\\boldsymbol{x}_i$ such the the first column is all one.\n",
    "<hr>\n",
    "The Python code at: https://github.com/ostad-ai/Machine-Learning\n",
    "<br> Explanation: https://www.pinterest.com/HamedShahHosseini/Machine-Learning/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "85af9aac",
   "metadata": {},
   "outputs": [],
   "source": [
    "# importing required modules\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "2acca7ef",
   "metadata": {},
   "outputs": [],
   "source": [
    "# least squares estimator for (p-1)-dimensional data points xi\n",
    "# computes pseudo-inverse of the given matrix X\n",
    "# we could simply use np.linalg.pinv(X)\n",
    "def pinverse(X):\n",
    "    return np.linalg.inv(X.T@X)@X.T\n",
    "\n",
    "# Xs is a matrix with n rows and p-1 columns\n",
    "# ys is a column vector of size n holding the dependent values yi\n",
    "def least_squares_estimator(Xs,ys):\n",
    "    X=np.ones((Xs.shape[0],Xs.shape[1]+1))\n",
    "    X[:,1:]=Xs.copy()\n",
    "    w=pinverse(X)@ys.reshape(-1,1)\n",
    "    return w.flatten()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "9dc89f5f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# example\n",
    "m,b,noise,Ndata,p=1.7,2.5,.2,100,2\n",
    "xs=np.random.rand(Ndata)\n",
    "Xs=xs.reshape(len(xs),p-1)\n",
    "ys=m*xs+b+noise*np.random.rand(Ndata)\n",
    "b_hat,m_hat=least_squares_estimator(Xs,ys)\n",
    "ys_hat=b_hat+m_hat*xs\n",
    "plt.plot(xs,ys,'.',label='Noisy data points')\n",
    "plt.plot(xs,ys_hat,'-',label='Least squares estimator')\n",
    "plt.xlabel('x'); plt.ylabel('y'); plt.legend()\n",
    "plt.title('Linear regression with least squares')\n",
    "plt.text(0,3.9,f'Real values: b={b:.2f}, m={m:.2f}')\n",
    "plt.text(0,3.8,f'Estimated: w0={b_hat:.2f}, w1={m_hat:.2f}')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c99ac4b8",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.11.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}