{ "cells": [ { "cell_type": "markdown", "id": "dedefa38", "metadata": {}, "source": [ "## Machine Learning\n", "### Gradient Descent for Linear and Ridge Regression\n", "In **Gradient Descent**, we move in the negative of gradient of the loss function in order to find the parameters that make the loss minimum. So, if the loss function is $L(\\boldsymbol{w})$, then we update the parameter vector $\\boldsymbol{w}$ by:\n", "
$\\boldsymbol{w}\\leftarrow \\boldsymbol{w}-\\eta_k\\nabla L(\\boldsymbol{w})$\n", "
where $\\eta_k>0$ is the **learning rate** (also called *step size*) at time step $k$.\n", "
In **Ridge regression**, we saw that we use the following loss function in which $\\frac{1}{2}$ is applied to make the fomulas simpler:\n", "
$L_{Ridge}(\\boldsymbol{w})=\\frac{1}{2}||\\boldsymbol{y}-X\\boldsymbol{w}||^2+\\frac{\\lambda}{2} ||\\boldsymbol{w}||^2$\n", "
If we set $\\lambda$ to zero, we get to the **linear regression**. Now, we compute $\\nabla L(\\boldsymbol{w})$ by:\n", "
$\\nabla L(\\boldsymbol{w})=-X^T(\\boldsymbol{y}-X\\boldsymbol{w})+\\lambda \\boldsymbol{w}$\n", "
**Reminder:** We have data points $(\\boldsymbol{x}_i,y_i)$ where the first components of $\\boldsymbol{x}_i$ are one. Thus, the rows of matrix $X$ are composed of $\\boldsymbol{x}^T_i$ such that the first column of $X$ is all one. Vectors denoted by bold symbols here are all column vectors.\n", "
In the following, \n", " - Gradient Descent (GD) for linear regression is implemented and tested for noisy data points of a line. \n", " - Then, Gradient Descent is implemented for ridge regression over noisy data points of a quadratic curve.\n", "\n", "
\n", "The Python code at: https://github.com/ostad-ai/Machine-Learning\n", "
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": "b9960049", "metadata": {}, "outputs": [], "source": [ "# Gradient Descent for linear Regression\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", "# etta is the learning for gradient descent\n", "def batchGD_LR(Xs,ys,iter=100,etta=.01):\n", " X=np.ones((Xs.shape[0],Xs.shape[1]+1))\n", " X[:,1:]=Xs.copy()\n", " w=np.random.rand(X.shape[1]).reshape(-1,1)\n", " for k in range(iter):\n", " w+=etta*X.T@(ys.reshape(-1,1)-X@w)\n", " return w.flatten()" ] }, { "cell_type": "code", "execution_count": 3, "id": "9dc89f5f", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# example of Gradient Descent (GD) for linear Regression\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=batchGD_LR(Xs,ys)\n", "xss=np.sort(xs)\n", "ys_hat=b_hat+m_hat*xss\n", "plt.plot(xs,ys,'.',label='Noisy data points')\n", "plt.plot(xss,ys_hat,'-',label='Batch GD')\n", "plt.xlabel('x'); plt.ylabel('y'); plt.legend()\n", "plt.title('Linear Regression with Gradient Descent')\n", "plt.text(0,4.,f'Real values: b={b:.2f}, m={m:.2f}')\n", "plt.text(0,3.9,f'Estimated: w0={b_hat:.2f}, w1={m_hat:.2f}')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "1f4c0cab", "metadata": {}, "source": [ "Now, we use Gradient Descent for Ridge Regression." ] }, { "cell_type": "code", "execution_count": 4, "id": "c99ac4b8", "metadata": {}, "outputs": [], "source": [ "# Gradient Descent (GD) for Ridge Regression\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", "# etta is the learning for gradient descent\n", "# landa is the ridge (regularization) parameter\n", "def batchGD_RR(Xs,ys,iter=100,etta=.01,landa=.1):\n", " X=np.ones((Xs.shape[0],Xs.shape[1]+1))\n", " X[:,1:]=Xs.copy()\n", " w=np.random.rand(X.shape[1]).reshape(-1,1)\n", " for k in range(iter):\n", " w+=etta*X.T@(ys.reshape(-1,1)-X@w)-etta*landa*w\n", " return w.flatten()" ] }, { "cell_type": "code", "execution_count": 5, "id": "dabb90b8", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# example of GD for Ridge Regression\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=batchGD_RR(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='Batch GD')\n", "plt.xlabel('x'); plt.ylabel('y'); plt.legend()\n", "plt.title('Ridge Regression with Gradient Descent')\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": "8b6d8a05", "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 }