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{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "dedefa38",
   "metadata": {},
   "source": [
    "## Machine Learning\n",
    "### Ridge regression with least squares\n",
    "In **Ridge Regression** similar to the *linear regression*, we use a linear model for the the data points:\n",
    "<br> $y=w_0+w_1x_1+w_2x_2+....w_{p-1}x_{p-1}$\n",
    "<br>Having data points $(\\boldsymbol{x}_i,y_i)$ we want to find the best estimate for parameter vector $\\boldsymbol{w}$ using the **least squares method** augmented with a penalty term called **regularization term** as shown below:<br>\n",
    "$L_{Ridge}(\\boldsymbol{w})=||\\boldsymbol{y}-X\\boldsymbol{w}||^2+\\lambda ||\\boldsymbol{w}||^2$\n",
    "<br>Minimizing the loss function $L_{Ridge}(\\boldsymbol{w})$ leads to: <br>\n",
    "$\\boldsymbol{w}=(X^TX+\\lambda I)^{-1}X^T\\boldsymbol{y}$ <br>\n",
    "where $I$ is the identity matrix, and $\\lambda\\ge0$ is the regularization (ridge) parameter.\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 the ridge matrix of the given matrix X\n",
    "def ridge_matrix(X,landa=.1):\n",
    "    p=X.shape[1]\n",
    "    I=np.identity(p)\n",
    "    return np.linalg.inv(X.T@X+landa*I)@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=ridge_matrix(X)@ys.reshape(-1,1)\n",
    "    return w.flatten()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "04d461ad",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# example\n",
    "a,b,c,noise,Ndata,p=1.7,2.5,5.3,.2,100,3\n",
    "xs=np.random.rand(Ndata)\n",
    "Xs=np.zeros((len(xs),p-1))\n",
    "Xs[:,0]=xs.copy()\n",
    "Xs[:,1]=Xs[:,0]**2\n",
    "ys=a+b*xs+c*xs**2+noise*np.random.rand(Ndata)\n",
    "a_hat,b_hat,c_hat=least_squares_estimator(Xs,ys)\n",
    "xss=np.sort(xs)\n",
    "ys_hat=a_hat+b_hat*xss+c_hat*xss**2\n",
    "plt.plot(xs,ys,'.',label='Noisy data points')\n",
    "plt.plot(xss,ys_hat,'-',label='Least squares estimator')\n",
    "plt.xlabel('x'); plt.ylabel('y'); plt.legend()\n",
    "plt.title('Ridge regression with least squares')\n",
    "plt.text(0,7.9,f'Real values: a={a:.2f}, b={b:.2f}, c={c:.2f}')\n",
    "plt.text(0,7.5,f'Estimated: w0={a_hat:.2f}, w1={b_hat:.2f}, w2={c_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
}