{ "cells": [ { "cell_type": "markdown", "id": "201265c2-adab-41f9-9d92-3c579b8feebf", "metadata": {}, "source": [ "# **Lecture 4 example: Gradient method for parameter estimation**\n", ">\n", ">- NB: Even though the gradient estimation methods have been implemented in most of machine learning/regression method, it would be nice we know how it has been worked\n", ">- There are two types of gradient methods, determinstic and stochastic\n", ">- Think about their efficiency and accuracy, i.e., pros/cons\n" ] }, { "cell_type": "markdown", "id": "815bf2b2-35ee-4bef-94c1-8ebfa24e7ef4", "metadata": {}, "source": [ "## **PART I:** For this implementation, we are going to use the advertising dataset.\n", "\n", "This is a dataset that gives us the total sales for different products, after marketing them on Television, Radio and Newspaper. Using our algorithm, we can find out which medium performs the best for our sales and assign weights to all the mediums accordingly." ] }, { "cell_type": "code", "execution_count": 74, "id": "fa0e4b9f-c93f-4bc3-a3ef-17a3e78bb12f", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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Unnamed: 0TVradionewspapersales
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" ], "text/plain": [ " Unnamed: 0 TV radio newspaper sales\n", "0 1 230.1 37.8 69.2 22.1\n", "1 2 44.5 39.3 45.1 10.4\n", "2 3 17.2 45.9 69.3 9.3\n", "3 4 151.5 41.3 58.5 18.5\n", "4 5 180.8 10.8 58.4 12.9" ] }, "execution_count": 74, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# load some necessary libraries\n", "import pandas as pd\n", "from numpy.random import randint\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import seaborn as sn\n", "df=pd.read_csv('Advertising.csv')\n", "df.head()" ] }, { "cell_type": "code", "execution_count": 6, "id": "c2060e3d-64b4-4ff2-ab0d-8b3ecaa356d7", "metadata": {}, "outputs": [], "source": [ "X=df[['TV','radio','newspaper']]\n", "Y=df['sales']\n", "Y=np.array((Y-Y.mean())/Y.std())\n", "X=X.apply(lambda rec:(rec-rec.mean())/rec.std(),axis=0)" ] }, { "cell_type": "markdown", "id": "d239fc5d-f8eb-4a48-95c1-593fc4ebd1a0", "metadata": {}, "source": [ "**Once we have a normalised dataset, we can start defining our algorithm. To implement a gradient descent algorithm we need to follow 4 steps:**\n", ">\n", ">- Randomly initialize the bias and the weight theta\n", ">- Calculate predicted value of y that is Y given the bias and the weight\n", ">- Calculate the cost function from predicted and actual values of Y\n", ">- Calculate gradient and the weights\n", ">" ] }, { "cell_type": "code", "execution_count": 9, "id": "b6d18180-d50e-4837-a8af-288fc26bf5b9", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Bias: 0.9526887046636117 , Weights: [0.01683829 0.6870954 0.50098462]\n" ] } ], "source": [ "import random\n", "def initialize(dim):\n", " b=random.random()\n", " theta=np.random.rand(dim)\n", " return b,theta\n", "\n", "b,theta=initialize(3)\n", "print(\"Bias: \",b, \", \", \"Weights: \",theta)" ] }, { "cell_type": "code", "execution_count": 11, "id": "397b5aef-62e5-4932-8f40-8c5095851bb9", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 2.53068341, 2.00931635, 2.8660883 , 2.43110685, 1.02304367,\n", " 3.13437818, 1.21417681, 0.3418495 , -0.73375777, -0.20844808])" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def predict_Y(b,theta,X):\n", " return b + np.dot(X,theta)\n", "\n", "Y_hat=predict_Y(b,theta,X)\n", "Y_hat[0:10]" ] }, { "cell_type": "code", "execution_count": 19, "id": "40bdbfe4-1a5b-4fe1-8261-b8d6c4a66793", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.8254478835326722" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import math\n", "def get_cost(Y,Y_hat):\n", " Y_resd=Y-Y_hat\n", " return np.sum(np.dot(Y_resd.T,Y_resd))/len(Y-Y_resd)\n", "\n", "Y_hat=predict_Y(b,theta,X)\n", "get_cost(Y,Y_hat)" ] }, { "cell_type": "markdown", "id": "f8cf321b-2ef8-49e0-b5f2-a73d10eb9b70", "metadata": {}, "source": [ "**NB: The parameters passed to the function are**\n", ">\n", ">- x,y : the input and output variable\n", ">- y_hat: predicted value with current bias and weights\n", ">- b_0,theta_0: current bias and weights\n", ">- Learning rate: learning rate to adjust the update step\n", ">" ] }, { "cell_type": "code", "execution_count": 22, "id": "ad3104d1-80c7-40df-9ace-40f82b0b992c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "After initialization -Bias: 0.9526887046636117 theta: [0.01683829 0.6870954 0.50098462]\n", "After first update -Bias: 0.9336349305703394 theta: [0.03075531 0.68134039 0.49069747]\n" ] }, { "data": { "text/plain": [ "1.8254478835326722" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def update_theta(x,y,y_hat,b_0,theta_o,learning_rate):\n", " db=(np.sum(y_hat-y)*2)/len(y)\n", " dw=(np.dot((y_hat-y),x)*2)/len(y)\n", " b_1=b_0-learning_rate*db\n", " theta_1=theta_o-learning_rate*dw\n", " return b_1,theta_1\n", "\n", "print(\"After initialization -Bias: \",b,\"theta: \",theta)\n", "Y_hat=predict_Y(b,theta,X)\n", "b,theta=update_theta(X,Y,Y_hat,b,theta,0.01)\n", "print(\"After first update -Bias: \",b,\"theta: \",theta)\n", "get_cost(Y,Y_hat)" ] }, { "cell_type": "code", "execution_count": 44, "id": "d68ab27d-c7e5-4f03-82c3-02c8ff36e8ac", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Final Estimate of b and theta is: 0.3364027827437597 [0.46412853 0.2043997 0.13832669]\n" ] } ], "source": [ "def run_gradient_descent(X,Y,alpha,num_iterations):\n", " b,theta=initialize(X.shape[1])\n", " iter_num=0\n", " gd_iterations_df=pd.DataFrame(columns=['iteration','cost'])\n", " result_idx=0\n", " for each_iter in range(num_iterations):\n", " Y_hat=predict_Y(b,theta,X)\n", " this_cost=get_cost(Y,Y_hat)\n", " prev_b=b\n", " prev_theta=theta\n", " b,theta=update_theta(X,Y,Y_hat,prev_b,prev_theta,alpha)\n", " if((iter_num%10==0)):\n", " gd_iterations_df.loc[result_idx]=[iter_num,this_cost]\n", " result_idx=result_idx+1\n", " iter_num +=1\n", " print(\"Final Estimate of b and theta is: \",b,theta)\n", " return gd_iterations_df,b,theta\n", "\n", "gd_iterations_df,b,theta=run_gradient_descent(X,Y,alpha=0.001,num_iterations=200)" ] }, { "cell_type": "code", "execution_count": 45, "id": "b89f0416-0482-417b-85e5-cffdf7a0fc63", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " iteration cost\n", "0 0.0 0.762186\n", "10 10.0 0.736024\n", "20 20.0 0.710951\n", "30 30.0 0.686920\n", "40 40.0 0.663886\n", "50 50.0 0.641806\n", "60 60.0 0.620638\n", "70 70.0 0.600343\n", "80 80.0 0.580883\n", "90 90.0 0.562223" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "gd_iterations_df[0:10]" ] }, { "cell_type": "code", "execution_count": 46, "id": "2d5a5212-627a-4a7f-8ddc-c1bbb6a697ff", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Cost or MSE')" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "plt.plot(gd_iterations_df['iteration'],gd_iterations_df['cost'])\n", "plt.xlabel(\"Number of iterations\")\n", "plt.ylabel(\"Cost or MSE\")" ] }, { "cell_type": "code", "execution_count": 47, "id": "72d7b828-06a9-4521-ac72-fef6a7d05558", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Final Estimate of b and theta is: 2.7774630888127755e-16 [ 0.75306591 0.53648155 -0.00433069]\n", "Final Estimate of b and theta is: 0.015495503503709054 [0.74481196 0.50267295 0.03065355]\n" ] }, { "data": { "text/plain": [ "Text(0.5, 1.0, 'Cost Vs. Iterations for different alpha values')" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "alpha_df_1,b,theta=run_gradient_descent(X,Y,alpha=0.01,num_iterations=2000)\n", "alpha_df_2,b,theta=run_gradient_descent(X,Y,alpha=0.001,num_iterations=2000)\n", "plt.plot(alpha_df_1['iteration'],alpha_df_1['cost'],label=\"alpha=0.01\")\n", "plt.plot(alpha_df_2['iteration'],alpha_df_2['cost'],label=\"alpha=0.001\")\n", "plt.legend()\n", "plt.ylabel('cost')\n", "plt.xlabel('Number of iterations')\n", "plt.title('Cost Vs. Iterations for different alpha values')" ] }, { "cell_type": "markdown", "id": "791f2ae7-d035-4feb-977f-9addfdcbd2e5", "metadata": {}, "source": [ "## ***Part II:*** demonstration of stochastic gradient\n", "\n", "A good reference to work on: https://jcboyd.github.io/assets/lsml2018/stochastic_gradient_descent.html" ] }, { "cell_type": "code", "execution_count": 48, "id": "af8fd836-2320-4211-b8f3-390e2470468e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "X_train shape: (10000, 100)\n", "y_train shape: (10000, 1)\n", "X_test shape: (100000, 100)\n", "y_test shape: (100000, 1)\n" ] } ], "source": [ "from scipy import io\n", "from numpy import log, exp\n", "\n", "data = io.loadmat('data_orsay_2017.mat')\n", "\n", "X_train, y_train = data['Xtrain'], data['ytrain']\n", "X_test, y_test = data['Xtest'], data['ytest']\n", "\n", "print('X_train shape: %s' % str(X_train.shape))\n", "print('y_train shape: %s' % str(y_train.shape))\n", "print('X_test shape: %s' % str(X_test.shape))\n", "print('y_test shape: %s' % str(y_test.shape))" ] }, { "cell_type": "code", "execution_count": 50, "id": "4bebf205-675e-479c-9fc1-713bf5715cfe", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "((10000, 101), (100000, 101))" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# This is to convert the data structure to X= [1, x]\n", "X_train_bt = np.concatenate([np.ones((X_train.shape[0], 1)), X_train], axis=1)\n", "X_test_bt = np.concatenate([np.ones((X_test.shape[0], 1)), X_test], axis=1)\n", "X_train_bt.shape, X_test_bt.shape " ] }, { "cell_type": "markdown", "id": "3f3a30b6-fb26-4f2c-b892-ae718aecf5aa", "metadata": {}, "source": [ "Defind the logical loss function: $Loss = \\frac{1}{N}\\sum_{i=1}^N\\log(1 + \\exp(-y_i\\mathbf{x}^T\\boldsymbol\\beta))$\n" ] }, { "cell_type": "code", "execution_count": 61, "id": "0aa52704-6a50-4bfc-a31b-459d73195fb6", "metadata": {}, "outputs": [], "source": [ "# Defind the logical loss function: $\\frac{1}{N}\\sum_{i=1}^N\\log(1 + \\exp(-y_i\\mathbf{x}^T\\boldsymbol\\beta))$\n", "\n", "def log_loss(X, y, beta):\n", " #TODO: implement the logistic loss function\n", " return np.sum(np.log(1 + np.exp(-y * X.dot(beta)))) / X.shape[0]\n", "\n", "\n", "# Implement a function to return the logistic loss gradient:\n", "def evaluate_gradient(X, y, beta):\n", " # TODO: implement the gradient of the logistic loss\n", " return np.sum(-X * y / (1 + np.exp(y * X.dot(beta))), axis=0) / X.shape[0]" ] }, { "cell_type": "markdown", "id": "bdca4544-a975-4f38-b61a-c1a0cf6b28e0", "metadata": {}, "source": [ "### **NB:** Stochastics gradient descent \n", "\n", "since the Dim(X), number of samples, is 10000, we will have to use the stochastic gradient descent" ] }, { "cell_type": "code", "execution_count": 86, "id": "8571b57d-c62e-4f64-9ce3-fb0ffe52030b", "metadata": {}, "outputs": [], "source": [ "# Pay attention to the generated radom vector for batch as stochastic gradient\n", "def minibatch_gradient_descent(X, y, batch_size=10, lr=1e-1, max_iters=1000, tol=1e-5):\n", " # randomly initialise beta\n", " N, D = X.shape\n", " beta = np.random.rand(D, 1)\n", " # initialise history variables\n", " losses = [log_loss(X, y, beta)]\n", " betas = [beta]\n", "\n", " for i in range(max_iters):\n", " # TODO: construct batch\n", " start = i * batch_size % N\n", " end = min(start + batch_size, N)\n", " idx = np.arange(start, end)\n", " batchX = X[idx]\n", " batchY = y[idx]\n", " grad = evaluate_gradient(batchX, batchY, beta)\n", " grad = grad[:, np.newaxis]\n", " # TODO: perform gradient descent step (as before)\n", " beta -= lr * grad\n", " if i % 10 == 0:\n", " loss = log_loss(X, y, beta)\n", " losses.append(loss)\n", " betas.append(beta.copy())\n", "\n", " if np.sqrt(grad.T.dot(grad)) < tol: break\n", "\n", " return betas, losses\n", "\n", "\n", "#Another way of random sampling\n", "\n", "def minibatch_gradient_descent_sampling(X, y, batch_size=10, lr=1e-1, max_iters=1000, tol=1e-5):\n", " # randomly initialise beta\n", " N, D = X.shape\n", " beta = np.random.rand(D, 1)\n", " # initialise history variables\n", " losses = [log_loss(X, y, beta)]\n", " betas = [beta]\n", "\n", " for i in range(max_iters):\n", " # TODO: randomly sample batch\n", " idx = np.random.randint(X.shape[0], size=batch_size)\n", " batchX = X[idx]\n", " batchY = y[idx]\n", " grad = evaluate_gradient(batchX, batchY, beta)\n", " grad = grad[:, np.newaxis]\n", " # TODO: perform gradient descent step (as before)\n", " beta -= lr * grad\n", " if i % 10 == 0:\n", " loss = log_loss(X, y, beta)\n", " losses.append(loss)\n", " betas.append(beta.copy())\n", "\n", " if np.sqrt(grad.T.dot(grad)) < tol: break\n", "\n", " return betas, losses\n", "\n", "# Run batch gradient descent\n", "betas, losses = minibatch_gradient_descent(X_train_bt, y_train, batch_size=10, lr=1e-0)" ] }, { "cell_type": "code", "execution_count": 71, "id": "4f536a5d-bcd6-4ec5-b10b-4b58f356b68f", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.76615" ] }, "execution_count": 71, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Check the accuracy of the predicted model using test data\n", "from scipy.special import expit\n", "beta = betas[-1]\n", "# TODO: calculate output probabilities\n", "probs = expit(X_test_bt.dot(beta))\n", "\n", "y_pred = list(map(lambda x : 1 if x >= 0.5 else -1, probs))\n", "\n", "from sklearn.metrics import accuracy_score\n", "accuracy_score(y_test, y_pred)" ] }, { "cell_type": "code", "execution_count": 72, "id": "cd1c7be6-2543-44c7-b540-8ce86bf4fc20", "metadata": {}, "outputs": [], "source": [ "### Now we start to investigate the impact of batch size to the convergency of results" ] }, { "cell_type": "code", "execution_count": 73, "id": "f414981e-5e4a-455a-8d72-a32e1adc9b34", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "bs = [1, 5, 100]\n", "_, losses1 = minibatch_gradient_descent(X_train, y_train, batch_size=bs[0])\n", "_, losses2 = minibatch_gradient_descent(X_train, y_train, batch_size=bs[1])\n", "_, losses3 = minibatch_gradient_descent(X_train, y_train, batch_size=bs[2])\n", "\n", "# create figure\n", "fig = plt.figure(figsize=(5, 5))\n", "# add subplot (rows, cols, number)\n", "ax = fig.add_subplot(1, 1, 1, xlabel='iteration', ylabel='loss')\n", "# plot data on new axis\n", "ax.plot(losses1, color='red', marker='.', alpha=0.5, label='M = %s'%bs[0])\n", "ax.plot(losses2, color='green', marker='.', alpha=0.5, label='M = %s'%bs[1])\n", "ax.plot(losses3, color='blue', marker='.', alpha=0.5, label='M = %s'%bs[2])\n", "ax.set_title('Stochastic gradient descent')\n", "# display lengend\n", "plt.legend()\n", "# display plot\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "73210685-28ce-45ea-afdc-f9adab4efbdf", "metadata": {}, "source": [ "## **PART III:** Two SGD are used based on their sampling methods, i.e., cycling vs random sampling\n", "**Below we will compare them**" ] }, { "cell_type": "code", "execution_count": 105, "id": "008421f6-7881-4b27-90c2-97612c3037b0", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "bs = [1, 10]\n", "betas1, losses1 = minibatch_gradient_descent(X_train, y_train, batch_size=bs[0])\n", "betas2, losses2 = minibatch_gradient_descent_sampling(X_train, y_train, batch_size=bs[0])\n", "betas3, losses3 = minibatch_gradient_descent(X_train, y_train, batch_size=bs[1])\n", "betas4, losses4 = minibatch_gradient_descent_sampling(X_train, y_train, batch_size=bs[1])\n", "\n", "# create figure\n", "fig = plt.figure(figsize=(10, 10))\n", "# add subplot (rows, cols, number)\n", "ax = fig.add_subplot(1, 1, 1, xlabel='iteration', ylabel='loss')\n", "# plot data on new axis\n", "ax.plot(losses1, color='red', marker='.', alpha=0.5, label='Cycling (M = %d)' % bs[0])\n", "ax.plot(losses2, color='blue', marker='.', alpha=0.5, label='Sampling (M = %d)' % bs[0])\n", "ax.plot(losses3, color='red', marker='*', alpha=0.5, label='Cycling (M = %d)' % bs[1])\n", "ax.plot(losses4, color='blue', marker='*', alpha=0.5, label='Sampling (M = %d)' % bs[1])\n", "# display plot\n", "ax.set_title('Cycling vs. sampling minibatch gradient descent')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 106, "id": "0bc16f9b-8615-4edf-8a5c-3f92258dad61", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(1001, 1001)" ] }, "execution_count": 106, "metadata": {}, "output_type": "execute_result" } ], "source": [ "len(betas3),len(betas1)" ] } ], "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": "3.9.13" }, "widgets": { "application/vnd.jupyter.widget-state+json": { "state": {}, "version_major": 2, "version_minor": 0 } } }, "nbformat": 4, "nbformat_minor": 5 }