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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<center> <h1>EE 526X Homework 01</h1> </center>\n",
"* Name: Xiaoshi Guo"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import pandas as pd\n",
"import matplotlib.pyplot as plt \n",
"from matplotlib import pylab"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Problem1 \n",
"\n",
"## a) Generate 51 equally weighted spaced x values between 0 and 1"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[0. 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26\n",
" 0.28 0.3 0.32 0.34 0.36 0.38 0.4 0.42 0.44 0.46 0.48 0.5 0.52 0.54\n",
" 0.56 0.58 0.6 0.62 0.64 0.66 0.68 0.7 0.72 0.74 0.76 0.78 0.8 0.82\n",
" 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1. ]\n"
]
}
],
"source": [
"X = np.arange(0,1+1/50,1/50)\n",
"print(X)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## b) Generate $y_i$ values for these $x_i$ values"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"E = np.random.normal(0, 1, X.size)\n",
"F_X = 1 + 2*np.sin(5*X) - np.sin(15*X)\n",
"Y = F_X + E"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## c) Fit a polynomial of order k = 1 to the dataset, minimizing the residual sum of squares. Plot the fitted polynomial using black color."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[ 3.00434105 -4.14181286]\n"
]
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Method 1 \n",
"X0 = np.ones(len(X))\n",
"X1 = np.column_stack((X0,X)) # 1 is in the first column \n",
"B = np.dot(np.dot(np.linalg.inv(np.dot(X1.T,X1)), X1.T), Y)\n",
"print(B)\n",
"# plot the fitted polynomial \n",
"plt.scatter(X, Y, color = \"blue\")\n",
"plt.plot(X, B[0]+B[1]*X, color='black')\n",
"plt.xlabel('x')\n",
"plt.ylabel('y')\n",
"pylab.title('Polynomial Fit with Matplotlib with Order = 1')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[-4.14181286 3.00434105]\n",
" \n",
"-4.142 x + 3.004\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Method 2 \n",
"# fit the polynomial of order 1 \n",
"z = np.polyfit(X,Y,1) \n",
"print(z) \n",
"\n",
"# find the coefficient of polynomial regression\n",
"p = np.poly1d(z)\n",
"print(p)\n",
"\n",
"# calculate new Y\n",
"Y_new = p(X)\n",
"\n",
"\n",
"# plot the fitted polynomial \n",
"plt.scatter(X, Y, color = \"blue\")\n",
"plt.plot(X, Y_new, color='black')\n",
"plt.xlabel('x')\n",
"plt.ylabel('y')\n",
"pylab.title('Polynomial Fit with Matplotlib with Order = 1')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## d) Repeat the steps (b) to (c) 30 times. Keep all the plotted polynomials."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"for t in range(1,31):\n",
" E = np.random.normal(0, 1, X.size)\n",
" F_X = 1 + 2*np.sin(5*X) - np.sin(15*X)\n",
" Y = F_X + E\n",
" X0 = np.ones(len(X))\n",
" X1 = np.column_stack((X0,X)) # 1 is in the first column \n",
" B = np.dot(np.dot(np.linalg.inv(np.dot(X1.T,X1)), X1.T), Y)\n",
" B = np.dot(np.linalg.pinv(X1),Y)\n",
" # plot the fitted polynomial \n",
" plt.plot(X, B[0]+B[1]*X, color='black')\n",
" plt.xlabel('x')\n",
" plt.ylabel('y')\n",
" pylab.title('Polynomial Fit with Matplotlib with Order = 1 for 30 Times')\n",
"plt.show()\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## e) Repeat the experiment for k = 3, 5, 7, 9, 11. For each k, use a new figure. Also, on each figure, show the function f(x) using red color."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Method 1\n",
"# define polynomial regression to get the coefficient \n",
"def polynomial_regression(X,Y,K):\n",
" X0 = np.ones(len(X))\n",
" X1 = np.column_stack((X0,X))\n",
" if K == 1:\n",
" B = np.dot(np.dot(np.linalg.inv(np.dot(X1.T,X1)), X1.T), Y)\n",
" else: \n",
" for k in range(2,K+1):\n",
" X1 = np.column_stack((X1,X**k)) # add one column for x**k\n",
" B = np.dot(np.dot(np.linalg.inv(np.dot(X1.T,X1)), X1.T), Y)\n",
" return B\n",
"\n",
"\n",
"# draw the polynomial plot\n",
"def poly_plot(X,K):\n",
" for t in range(1,31):\n",
" E = np.random.normal(0, 1, X.size)\n",
" F_X = 1 + 2*np.sin(5*X) - np.sin(15*X)\n",
" Y = F_X + E\n",
" B = polynomial_regression(X,Y,K)\n",
" y = B[0]\n",
" for i in range(1,K+1):\n",
" y = y+B[i]*X**i\n",
" plt.plot(X, y, color = 'black')\n",
" plt.plot(X, F_X, color = 'red')\n",
" plt.xlabel('x')\n",
" plt.ylabel('y')\n",
" pylab.title('Polynomial Fit with Matplotlib with Order = %d for 30 Times' %K)\n",
" plt.show()\n",
" \n",
"\n",
"for k in [3,5,7,9,11]:\n",
" poly_plot(X,k)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## We can observe that, as the order of the polynomial functions increases, the complexity of function has increased as well. It can better describe the data, which can reduce the bias while adding the variance simultanouesly. Since the red curve is always in between the black curves when we increase the order, however, the black curves are not as close to each other as the black curves with order = 1. "
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Method 2\n",
"for k in [3,5,7,9,11]:\n",
" for t in range(1,31):\n",
" E = np.random.normal(0, 1, X.size)\n",
" F_X = 1 + 2*np.sin(5*X) - np.sin(15*X)\n",
" Y = F_X + E\n",
" # fit the polynomial of order 1 \n",
" z = np.polyfit(X,Y,k) \n",
"\n",
" # find the coefficient of polynomial regression\n",
" p = np.poly1d(z)\n",
"\n",
" # calculate new Y\n",
" Y_new = p(X)\n",
"\n",
" # plot the fitted polynomial \n",
" plt.plot(X, Y_new, color='black')\n",
" plt.plot(X, F_X, color='red')\n",
" plt.xlabel('x')\n",
" plt.ylabel('y')\n",
" pylab.title('Polynomial Fit with Matplotlib with order = %d' %k)\n",
" plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Problem 2\n",
"Use **_Python_** to implement the perceptron algorithm and test it on the following data: where there are 6 points, (x1, x2) is the input, and y is the binary output label.\n",
"\n",
"| | $$x_1$$ | $$x_2$$ | y |\n",
"|----|-------|-------|-----|\n",
"| 1 | 1 | 2 | 1 |\n",
"| 2 | 1 | 4 | 1 |\n",
"| 3 | 2 | 2 | 1 |\n",
"| 4 | 4 | 2 | -1 |\n",
"| 5 | 3 | 4 | -1 |\n",
"| 6 | 2 | 3 | -1 |\n",
"Initialize your algorithm with the vector\n",
"$$\\theta = [b,w_1,w_2]^\\top=[0,0,0]^\\top$$\n",
"Plot the points and the final hyperplane (a line) on the same graph."
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [],
"source": [
"# Answer: \n",
"from numpy import linalg as LA\n",
"def mysign(x):\n",
" if x>=0:\n",
" return 1\n",
" else:\n",
" return -1\n",
"\n",
"# define the perceptron algorithm \n",
"def perceptron_algorithm(X, Y, epochs = 1000):\n",
" w = np.zeros(X.shape[1]) #initialize w\n",
" w2 = np.zeros(X.shape[1])\n",
" eta = 1 # set the learning rate\n",
" \n",
" for t in range(epochs):\n",
" for i in range(0,len(X)):\n",
" # way 1\n",
" Y_hat = mysign(X[i].dot(w2))\n",
" w2 = w2 + eta*(Y[i]-Y_hat)*X[i] \n",
" \n",
" # way 2 \n",
" if (np.dot(X[i], w)*Y[i]) <= 0:\n",
" w = w + eta*X[i]*Y[i]\n",
" \n",
" return w\n",
"\n",
"\n",
"# give the input data\n",
"X = np.array([[1, 1, 2],[1,1, 4],[1, 2, 2],[1, 4, 2],[1, 3, 4],[1, 2, 3]])\n",
"Y = np.array([1,1,1,-1,-1,-1])"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[ 35. -15. -2.]\n",
"[ 35. -15. -2.]\n",
"[ 35. -15. -2.]\n",
"[ 35. -15. -2.]\n",
"[ 35. -15. -2.]\n",
"[ 35. -15. -2.]\n",
"[ 35. -15. -2.]\n",
"[ 35. -15. -2.]\n",
"[ 35. -15. -2.]\n"
]
}
],
"source": [
"# Test the convergence\n",
"for epochs in range(1000, 10000, 1000):\n",
" w = perceptron_algorithm(X, Y, epochs)\n",
" print(w)"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"W = perceptron_algorithm(X, Y, 1000)\n",
"\n",
"# plot the points \n",
"for d, sample in enumerate(X):\n",
" # Plot the positive samples\n",
" if d < 3:\n",
" plt.scatter(sample[1], sample[2], s=120, marker='_', \n",
" linewidths=2, color = 'red')\n",
" # Plot the negative samples\n",
" else:\n",
" plt.scatter(sample[1], sample[2], s=120, marker='+', \n",
" linewidths=2, color = 'green')\n",
"\n",
" \n",
"# plot the hyperplane\n",
"xmin, xmax = plt.xlim()\n",
"x = np.linspace(xmin,xmax,num=10)\n",
"w0 = W[0]\n",
"w1 = W[1]\n",
"w2 = W[2]\n",
"plt.plot(x, -(w1*x+w0)/w2, color = 'blue')\n",
"plt.title('Perceptron classifier(hyperplane in blue)')\n",
"plt.xlabel('$x_1$')\n",
"plt.ylabel('$x_2$')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## By increasing the epochs, we can find that the values of parameters will become stable, which means it converges at $\\theta = [35, -15, -2]$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Problem 3\n",
"The Spambase Data Set contains email spam data for 4601 email messages. Download the data from https://archive.ics.uci.edu/ml/datasets/spambase and divide the data into training set and test set. The training set should contain the first 2/3 of spam and ham (i.e., non-spam) messages. The test set should contain the last 1/3 spam and ham messages.\n",
"* (a) Write a logistic regression program (function) using gradient descent algorithm. And train the weights using training set and then test the result on the test set. Experiment with the step size (learning rate)."
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [],
"source": [
"# Load the data\n",
"uri = 'https://archive.ics.uci.edu/ml/machine-learning-databases/spambase/spambase.data'\n",
"df = pd.read_csv(uri, header=None)\n",
"df.head()\n",
"from sklearn.model_selection import train_test_split #so that we can split test and training data \n",
"X, Y = df.iloc[:,0:(df.shape[1]-1)], df.iloc[:,-1] # define X and Y\n",
"X_train, X_test, Y_train, Y_test = train_test_split(X,Y, test_size=1/3) # define training and test data. test_size is the size for the test data "
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [],
"source": [
"# define logistic regression algorithm\n",
"def log_reg(X_Train,Y_train,Step_Size, epochs = 10000):\n",
" theta = np.zeros(X_Train.shape[1])\n",
" m = X_Train.shape[0]\n",
" \n",
" for t in range(epochs):\n",
" p = 1/ (1+np.exp(-np.dot(X_Train, theta)))\n",
" gradient = 1/m * np.dot(X_Train.T,(np.array(p)-np.array(Y_train)))\n",
" theta = theta - Step_Size*(gradient.T)\n",
" \n",
" return theta"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {},
"outputs": [],
"source": [
"# define the function to predict y for the test data\n",
"def predict_y (X_test, theta):\n",
" y_hat = 1/ (1+np.exp(-np.dot(X_test,theta)))\n",
" y_hat[y_hat > 1/2] = 1\n",
" y_hat[y_hat <= 1/2] = 0\n",
" return y_hat"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {},
"outputs": [],
"source": [
"# Aplly log_reg on the training data\n",
"X_Train = np.concatenate((np.ones((X_train.shape[0],1)),X_train),axis=1)\n",
"X_Train = pd.DataFrame(X_Train)"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {},
"outputs": [],
"source": [
"# Define the loss function \n",
"def loss_function(X_Train, theta, y):\n",
" p = 1/ (1+np.exp(-np.dot(X_Train, theta)))\n",
" loss = 0\n",
" for i in range (0, len(y)):\n",
" if p [i] == 0 or p[i] == 1:\n",
" continue\n",
" loss += y [i] * np.log(p[i]) + (1 - p [i]) * np.log(1 - p [i])\n",
" return -loss"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The prediction accuracy rate is 86.83181225554108 %\n"
]
}
],
"source": [
"Theta = log_reg(X_Train,Y_train,0.0001,100000) # get the coefficient of the hyperplane \n",
"# Apply theta derived by training data on the test data \n",
"X_Test = np.concatenate((np.ones((X_test.shape[0],1)),X_test),axis=1)\n",
"#Y_Test = pd.DataFrame(X_Test)\n",
"Y_hat = predict_y(X_Test, Theta)\n",
"\n",
"\n",
"# get the accuracy\n",
"Accuracy = (Y_test == Y_hat).mean() * 100\n",
"print(f\"The prediction accuracy rate is {Accuracy} %\")"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0, 0.5, 'Accuracy (\\\\%)')"
]
},
"execution_count": 41,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# test for the step size and the accuracy \n",
"def exp_range(start, end, mul):\n",
" while start < end:\n",
" yield start\n",
" start *= mul\n",
"#print(list(exp_range(0.000001, 0.01, 10))) \n",
"\n",
"accuracy = []\n",
"S_s = []\n",
"for Step_size in exp_range(0.000001, 0.01, 10):\n",
" Theta = log_reg(X_Train, Y_train, Step_size, 90000)\n",
" Y_hat = predict_y(X_Test, Theta)\n",
" accuracy.append((Y_test == Y_hat).mean() * 100)\n",
" S_s.append(float(Step_size))\n",
"# print(accuracy)\n",
" \n",
"plt.plot(S_s, accuracy, 'r-')\n",
"plt.xlabel('Step Size')\n",
"plt.ylabel('Accuracy (\\%)')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"* (b) Next, normalize the features, so that each feature in the training data has mean 0 and variance 1. Then run logistic regression on the normalized data."
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"For the normalized data, the prediction accuracy rate is 89.56975228161669 %\n"
]
}
],
"source": [
"# normalize the features by substracting the mean of each column and dividing the standard deviation of each column\n",
"NX_train = (X_train - np.mean(X_train))/np.std(X_train) #normalize X \n",
"NX_Train = np.concatenate((np.ones((NX_train.shape[0],1)),NX_train),axis=1) #Add the first column to be 1 for X \n",
"NX_Train = pd.DataFrame(NX_Train)\n",
"\n",
"NX_test = (X_test - np.mean(X_test))/np.std(X_test) #Nomrlalize Y\n",
"NX_Test = np.concatenate((np.ones((NX_test.shape[0],1)),NX_test),axis=1) #Add the first column to be 1 for Y \n",
"NX_Test = pd.DataFrame(NX_Test)\n",
"\n",
"# get the coefficient of the hyperplane \n",
"Theta_N = log_reg(NX_Train,Y_train,0.0001,10000) \n",
"\n",
"# get the predicted Y for test\n",
"Y_hat_N = predict_y(NX_Test, Theta_N)\n",
"\n",
"# get the accuracy\n",
"Accuracy = (Y_test == Y_hat_N).mean() * 100\n",
"print(f\"For the normalized data, the prediction accuracy rate is {Accuracy} %\")"
]
},
{
"cell_type": "code",
"execution_count": 54,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0, 0.5, 'Accuracy (\\\\%)')"
]
},
"execution_count": 54,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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IIuLBFY9lvZC1IuLDiJhL3b0JgLskdQSWAqdFxHxJlwK3Z8NeM4HDsnuXAadExEnZ+56kOZUnV7jnKEmdAQETgVPqbaXV78474Y034MorvfrczFZKnXMkXzhROgk4ljRB/4+I+J88A2tMniOpRwTsvHOaI5k61ZPpZgaUPkdS638xJH1/hUP7RMR3ImJ34HsNDdCakccfh3/9C847z0nEzFZaXf/V2EHSvZJ2yN6/KGmUpHKg3ie2rAUZOhQ23TTVxjIzW0l1zZH8WtKmwC/TvDY/B9YH2tX1pJa1MC+8AH/7WyrvvnaNS3LMzOpU38r2j4GzgV6kNRvPA5flHZQ1ocsugw02gFP8zIKZrZq65kh+DTwIPA7sGREHAJOAByUd20TxWZ5efz3tXHjKKd6l0MxWWV1zJAMjoh+wG3AcQETcB+wHeLlza3DFFan8+1lnFR2JmbVgdQ1tTZZ0C7Au1dZyREQlcHXegVnO5s2Dm25KE+zduhUdjZm1YHVNth8j6RvA0oh4ecXPJXWNiNm5Rmf5ue46WLw4PfJrZtYAdU62R8RLVb9LWgP4NrA/qQz8e3g9Scv08cepsu8BB3g/ETNrsDoTSVYjqz8peWwOPA08AlwcEZ/kH57l4qabUnHG888vOhIzawXqqv77PDAbeBQ4NyJeb7KoLD+VlWmSfbfdXJzRzBpFXT2SvhHxaV0XS1KUWqzLmoc77oA334Rrrik6EjNrJep6/PcxSWdkw1ufkbSWpL0kjSSVgbeWIgKGDYOvfhUGDiw6GjNrJerqkfQHTgBGS9oSWEDa2Gp14DHgyoiYmH+I1mjGjk17sY8Y4eKMZtZo6nr89xPgD8AfJK0JdAIWR8SCpgrOGtmwYdC1K/zgB0VHYmatSH21tgDItrqdU++J1nxNmJDKxQ8b5uKMZtaoPL7RVlx2GWy4IQwZUnQkZtbKOJG0Ba++mp7WcnFGM8tBvYlE0umS2jdFMJaT3/0O1ljDxRnNLBel9Eg2BZ6XdLuk/sp2uSqFpLMkTZY0RdLZ2bEOksZKmp79rDFJSVomaWL2uq/a8S0lPZtdf5uktUqNp02qKs547LFpot3MrJHVm0gi4mekja1GAMcD0yX9RtJX6rpO0nbAyUAfYAdgoKRewIXA4xHRi7TXyYW13GJxRPTOXgdUOz6U9OhxL2A+cGJ9bWjTrr0WPvkEfvKToiMxs1aqpDmSbPX6O9mrEmgP3ClpWB2XbQuMj4hFWen5J4FBwIHAyOyckcBBpQab9Yb2Au5clevbnKrijAcemBYhmpnloJQ5kjMlTQCGkYo2fiMi/hvYGTikjksnA/0kdZTUDhgAdAc2iYg5ANnPLrVcv46kCknjJVUli47AgiwxAcwCatxMQ9KQ7PqKefPm1dfM1mnECHj/fRdnNLNclbKOpBNwcES8Wf1gRCyXVGudjYiYJmkoMBZYSNqmt7K282vQIyJmS9oKeELSS8CHNX1VLd8/nLTPPGVlZW2vHtjSpak447e/nQo0mpnlpJShrYeA96veSNpA0i6QkkVdF0bEiIjYKduy931gOvCupM2ye20GzK3l2tnZz9eAvwM7kvZA2TjbGwVSaXtvrlWTO+6AmTPdGzGz3JWSSP5I6lFU+Tg7Vi9JXbKfPYCDgdHAfXxe7HEwcG8N17WXtHb2eyegLzA1m6sZBxxa1/VtXlVxxm23he957zEzy1cpieQLpeIjYjklllYB7pI0FbgfOC0i5gOXAt+VNB34bvYeSWWSbsyu2xaokDSJlDgujYip2WcXAOdKmkGaMxlRYixtx2OPwaRJaRtdF2c0s5ypvu1EJN1NGlqq6oWcCuwZES3maamysrKoqKgoOoyms/fe8PLL8PrrsJaX2ZjZqpE0ISLK6juvlH+ungLsBrxNekpqF8AFm5qrigp44gk45xwnETNrEvUOUUXEXODIJojFGsOwYS7OaGZNqt5EImkd0urxr5M2tgIgIk7IMS5bFTNmwF13pbmRDTcsOhozayNKGdq6hVRvaz/S6vTNgY/yDMpWkYszmlkBSkkkW0fE/wM+joiRwPeAb+Qblq20uXPh5pvhuONgs82KjsbM2pBSEsnS7OeCrBDjRkDP3CKyVfP738OSJS7OaGZNrpT1IMOzUu8/Iy0mXB/4f7lGZStn4UK47rpUnPG//qvoaMysjakzkUhaDfgwW0j4FLBVk0RlK2fECJg/Hy64oOhIzKwNqnNoK1vFfnoTxWKrYunSNMm+++6w665FR2NmbVApcyRjJf1EUvdsd8MOkjrkHpmV5rbbXJzRzApVSomU12s4HBHRYoa5Wm2JlAjYYQdYtgxeesl1tcysUZVaIqWUle1bNk5I1ugefTQlkD//2UnEzApTysr242o6HhF/afxwbKUMGwbdusFRRxUdiZm1YaU8/vvNar+vA+wNvAA4kRTp+edh3Di4/HIXZzSzQpUytHVG9feSNiKVTbEiDRsGG20EJ59cdCRm1satysD6IqBXYwdiK6GqOOOpp7o4o5kVrpQ5kvuBqke7VgO+BtyeZ1BWjyuugDXXhDPPLDoSM7OS5kgur/Z7JfBmRMzKKR6rz7vvpuKMgwfDppsWHY2ZWUmJZCYwJyI+AZC0rqSeEfFGrpFZzX7/e/j0UxdnNLNmo5Q5kjuA5dXeL8uO1UvSWZImS5oi6ezsWAdJYyVNz362r+G63pKeya57UdIR1T77s6TXJU3MXr1LiaVVqCrOOGgQbLNN0dGYmQGlJZI1IuLTqjfZ7/U+b5qVnD8Z6APsAAyU1Au4EHg8InoBj2fvV7QIOC4ivg70B66StHG1z8+LiN7Za2IJbWgdbrwRFixwORQza1ZKSSTzJB1Q9UbSgcB7JVy3LTA+IhZFRCVpd8VBwIHAyOyckcBBK14YEf+OiOnZ77OBuUDnEr6z9aoqztivH+yyS9HRmJl9ppREcgrwP5JmSpoJXAD8qITrJgP9JHWU1A4YAHQHNomIOQDZzy513URSH1IP6NVqhy/JhryulLR2CbG0fGPGwFtvuTdiZs1OvUUbPztRWj87v+T92iWdCJwGLASmAouBH0bExtXOmR8RX5onyT7bDPg7MDgixlc79g4puQwHXo2IX9Zw7RBgCECPHj12fvPNN0sNu/mJgO23T7+/+CJIxcZjZm1CqUUb6+2RSPqNpI0jYmFEfCSpvaRflxJERIyIiJ0ioh/wPjAdeDdLBlVJYW4t37sh8CDws6okkt1zTiRLgJtJczA1fffwiCiLiLLOnVv4qNgjj8DkyXDeeU4iZtbslDK0tX9ELKh6k+2WOKCUm0vqkv3sARwMjCZt1zs4O2UwcG8N160F3AP8JSLuWOGzqiQk0vzK5FJiadGGDoXNN4cjjyw6EjOzLyllHcnqktbOegBIWhcodV7iLkkdgaXAaRExX9KlwO3ZsNdM4LDsvmXAKRFxEnA40A/oKOn47F7HZ09ojZLUGRAwkTSH03o9+yw8+WSaaHdxRjNrhkrZ2Op84ADSMFIAJwD3R8TQ/MNrHC16Y6tDD4XHH0+7IG6wQdHRmFkb0pgbWw2T9CKwD6kX8KuIeLQRYrT6TJ8Od98NP/2pk4iZNVulDG0REY8AjwBI6ivpuog4LdfI7PO9Rlyc0cyasZISSVaG5CjgCOB14O48gzLgnXdg5Eg4/njYZJOiozEzq1WtiUTSNsCRpATyH+A20pzKnk0UW9tWVZzxxz8uOhIzszrV1SN5GfgH8P2ImAEg6Zwmiaqt++gj+MMf4OCDoZf3EDOz5q2udSSHkFaQj5P0J0l7kybbLW9/+pOLM5pZi1FrIomIeyLiCOCrpDIl5wCbSPqjpH2bKL6259NP4corYY89oE+Ni/bNzJqVele2R8THETEqIgYCm5MWAdZU+t0aw5gxMGuWeyNm1mKUXLSxJWsxCxKXL0/FGSUXZzSzwjXagkRrQg8/DFOmwF/+4iRiZi1GKUUbrakMGwbdu7s4o5m1KO6RNBfjx8NTT6WJ9jXXLDoaM7OSuUfSXAwbBu3bw0knFR2JmdlKcSJpDl55Bf76Vzj1VFh//aKjMTNbKU4kzcEVV7g4o5m1WE4kRasqzvjDH0KXLkVHY2a20pxIinb11bB0qYszmlmL5URSpA8/hD/+EQ45BLbeuuhozMxWiRNJkf70J/jgA5dDMbMWLddEIuksSZMlTZF0dnasg6SxkqZnP9vXcu3g7JzpkgZXO76zpJckzZB0jdRCl4BXFWfcc0/45jeLjsbMbJXllkgkbQecDPQBdgAGSupFKvj4eET0Ah6nhgKQkjoAFwO7ZNdfXC3h/BEYAvTKXv3zakOubr0V3n7bvREza/Hy7JFsC4yPiEURUQk8CQwCDgRGZueMBA6q4dr9gLER8X5EzAfGAv0lbQZsGBHPRKo2+Zdarm/eli+Hyy5LBRr326/oaMzMGiTPRDIZ6Cepo6R2wACgO7BJRMwByH7W9MxrN+Ctau9nZce6Zb+veLxleeghmDo19UZa6MicmVmV3GptRcQ0SUNJvYmFwCSgssTLa/qva9Rx/Ms3kIaQhsDo0aNHiV/bRIYNgx494PDDi47EzKzBcp1sj4gREbFTRPQD3gemA+9mQ1RkP+fWcOksUu+lyubA7Oz45jUcr+m7h0dEWUSUde7cueGNaSzPPAP/+Aece66LM5pZq5D3U1tdsp89gIOB0cB9QNVTWIOBe2u49FFgX0nts0n2fYFHs6GwjyTtmj2tdVwt1zdfVcUZTzyx6EjMzBpF3utI7pI0FbgfOC2bOL8U+K6k6cB3s/dIKpN0I0BEvA/8Cng+e/0yOwbw38CNwAzgVeDhnNvQeF5+Ge69F04/3cUZzazV8Fa7Tenkk6G8HN5803W1zKzZK3WrXa9sbypz5qQtdF2c0cxaGSeSpnL11VBZ6eKMZtbqOJE0harijIceCl/5StHRmJk1KieSpjB8eEom551XdCRmZo3OiSRvS5ak4ox77QVl9c5ZmZm1OLmtbLfMrbfC7Nlw001FR2Jmlgv3SPJUVZxxhx1g332LjsbMLBfukeTpwQdh2jQYNcrFGc2s1XKPJE9Dh8IWW8BhhxUdiZlZbtwjycvTT6fX1Ve7OKOZtWrukeTlssugQwcXZzSzVs+JJA/VizOut17R0ZiZ5cqJJA+XXQbrrJMSiZlZK+dE0thmz4ZbboETToDmtKGWmVlOnEga29VXw7JlLs5oZm2GE0lj+uADuP769LjvVlsVHY2ZWZNwImlMN9zg4oxm1uY4kTSWJUvgqqtg771h552LjsbMrMl4QWJjGTUq7YI4cmTRkZiZNalceySSzpE0RdJkSaMlrSNpL0kvZMdGSvpSMpO0p6SJ1V6fSDoo++zPkl6v9lnvPNtQkqrijL17wz77FB2NmVmTyi2RSOoGnAmURcR2wOrA0cBI4Mjs2JvA4BWvjYhxEdE7InoDewGLgMeqnXJe1ecRMTGvNpTs/vvTIsTzz3dxRjNrc/KeI1kDWDfrdbQDPgaWRMS/s8/HAofUc49DgYcjYlF+YTbQsGHQs6eLM5pZm5RbIomIt4HLgZnAHOAD4HZgTUlVWwUeCnSv51ZHAqNXOHaJpBclXSlp7UYMe+U9/TT8859p3cgannIys7Ynz6Gt9sCBwJZAV2A94AekxHClpOeAj4DKOu6xGfAN4NFqh38KfBX4JtABuKCWa4dIqpBUMW/evIY3qDbDhkHHjvDDH+b3HWZmzVieQ1v7AK9HxLyIWArcDewWEc9ExO4R0Qd4Cphexz0OB+7JrgcgIuZEsgS4GehT04URMTwiyiKirHNepUqmToX77nNxRjNr0/JMJDOBXSW1kyRgb2CapC4A2ZDUBcD1ddzjKFYY1sp6KWT3PAiYnEPspbn8clh3XRdnNLM2Lc85kmeBO4EXgJey7xoOnCdpGvAicH9EPAEgqUzSjVXXS+pJmj95coVbj5L0UnbPTsCv82pDnd5+G8rL034jnToVEoKZWXOgiCg6htyVlZVFRUVF4970/PPhiitgxgzYcsvGvbeZWTMgaUJElNV3nkukrIoFC1JxxsMPdxIxszbPiWRV3HADfPRR6pWYmbVxTiQrq6o443e/CzvuWHQ0ZmaF8wq6lVVeDu+8k3ZBNDMz90ijXkd1AAAI50lEQVRWSlVxxh13TOXizczMPZKVct998MorMHq0izOamWXcIylVBAwdmp7SOvTQoqMxM2s23CMp1dNPw/jxcO21Ls5oZlaNeySlGjrUxRnNzGrgRFKKKVPggQfgjDOgXbuiozEza1acSEpx+eUpgbg4o5nZlziR1GfWLBg1KhVn7Nix6GjMzJodJ5L6XHVVWj9y7rlFR2Jm1iw5kdRlwYJUV+vww9Oe7GZm9iVOJHW5/npYuNDFGc3M6uBEUpdNN4UTToDevYuOxMys2fLKurocf3x6mZlZrdwjMTOzBnEiMTOzBsk1kUg6R9IUSZMljZa0jqS9JL2QHRspqcbhNUnLJE3MXvdVO76lpGclTZd0m6S18myDmZnVLbdEIqkbcCZQFhHbAasDRwMjgSOzY28Cg2u5xeKI6J29Dqh2fChwZUT0AuYDJ+bVBjMzq1/eQ1trAOtmvY52wMfAkoj4d/b5WOCQUm8mScBewJ3ZoZHAQY0XrpmZrazcEklEvA1cDswE5gAfALcDa0oqy047FOheyy3WkVQhabykqmTREVgQEZXZ+1lAt1waYGZmJcnt8V9J7YEDgS2BBcAdwA+AI4ErJa0NPAZU1nKLHhExW9JWwBOSXgI+rOG8qOX7hwBDAHr06NGQppiZWR3yHNraB3g9IuZFxFLgbmC3iHgmInaPiD7AU8D0mi6OiNnZz9eAvwM7Au8BG1eboN8cmF3L9cMjoiwiyjp37tyY7TIzs2ryXJA4E9hVUjtgMbA3UCGpS0TMzXokFwCXrHhh1ptZFBFLJHUC+gLDIiIkjSMNiY0hTdTfW18gEyZMeE/Sm/Wc1omUqNoSt7ltcJtbv7zau0UpJymixpGhRiHpF8ARpOGrfwEnAb8GBpJ6Q3+MiKuyc8uAUyLiJEm7ATcAy7PzroqIEdl5W5GSSIfsnsdExJJGiLUiIsrqP7P1cJvbBre59Su6vbkmkpak6D+IIrjNbYPb3PoV3V6vbDczswZxIvnc8KIDKIDb3Da4za1foe310JaZmTWIeyRmZtYgrTaRSOov6RVJMyRdWMPna2dFH2dkRSB7Vvvsp9nxVyTtV+o9i5RTe2+SNFfS5KZpxcpp7DZL6i5pnKRpWbHRs5quNaXJoc3rSHpO0qSszb9outaUJo+/29lnq0v6l6QH8m/Fysnp/89vSHpJqRBuRaMGHBGt7kUqEPkqsBWwFjAJ+NoK55wKXJ/9fiRwW/b717Lz1yatyn81u1+992xN7c0+6wfsBEwuuo1N9Ge8GbBTds4GwL+by59xjm0WsH52zprAs8CuRbc177/b2efnArcCDxTdzqZoM/AG0CmPmFtrj6QPMCMiXouIT0nrTg5c4ZwDSUUfIRWB3FuSsuNjImJJRLwOzMjuV8o9i5JHe4mIp4D3m6IBq6DR2xwRcyLiBYCI+AiYRvOq5ZZHmyMiFmbnr5m9mtPEaS5/tyVtDnwPuLEJ2rCycmlznlprIukGvFXtfU3FHT87J1IRyA9IRSFru7aUexYlj/Y2d7m2ORsq2JH0L/TmIpc2Z0M8E4G5wNiIaPVtBq4Czictem5u8mpzAI9JmqBUi7DRtNZEohqOrfivrNrOWdnjzUEe7W3ucmuzpPWBu4CzI6KmQqFFyaXNEbEsInqTatf1kbRdg6JsXI3eZkkDgbkRMaGhweUkr7/bfSNiJ2B/4DRJ/VY9xC9qrYlkFl8sT19TccfPzlEqArkRaRintmtLuWdR8mhvc5dLmyWtSUoioyLi7lwiX3W5/jlHxAJSgdT+jRl0A+XR5r7AAZLeIA0b7SWpPI/gV1Euf87xeSHcucA9NOaQV9ETS3m8SMUoXyNNNlVNVn19hXNO44uTVbdnv3+dL05WvUaa/Kr3nq2pvdWu60nznGzP489YwF9Itd0Kb2MTtbkzsHF2zrrAP4CBRbe1Kf5uZ+fsQfObbM/jz3k9YIPsnPWAfwL9Gy3mov9Hy/EPYwDpqZtXgYuyY78EDsh+X4e0R8oM4Dlgq2rXXpRd9wqwf133bC6vnNo7mrQp2VLSv3ROLLqdebYZ+DZpGOBFYGL2GlB0O3Nu8/ak4qcvApOBnxfdxqb4u13t8z1oZokkpz/nrUgJZhIwpbH/++WV7WZm1iCtdY7EzMyaiBOJmZk1iBOJmZk1iBOJmZk1iBOJmZk1iBOJWQkkXZRVx30xq566S3b8bEntGuk7NpH0QFaJd6qkh7LjXSXd2RjfYZYHP/5rVg9J3wJ+B+wREUskdQLWiojZ2erosoh4rxG+5wZgakRcnb3fPiJebOh9zfLmHolZ/TYD3ouIJQAR8V6WRM4EugLjJI0DkLSvpGckvSDpjqxuV9VeEEOzvT+ek7R1Ld8zq+pNVRKR1FPZnjCSbsx6RBMlzZN0cXb8PEnPZz2mZreniLVuTiRm9XsM6C7p35L+IOk7ABFxDamO0Z4RsWfWU/kZsE+k4ngVpD0vqnwYEX2Aa0nVZ1d0HTBCaXOtiyR1XfGEiDgpUoHFA4H/AH+WtC/Qi1Q7qTewc2MW5DOrjxOJWT0i7dexMzAEmAfcJun4Gk7dlbSx0NNZWfbBwBbVPh9d7ee3avieR0mlLP4EfBX4l6TOK54nqao8xukR8Sawb/b6F/BCdm2vlW6o2Spao+gAzFqCiFhGqoz7d0kvkZLEn1c4TaT9PI6q7Ta1/F79e94n7dp3a7YFbD9gxXLn1wN3R8Tfqn3vbyPihtJaY9a43CMxq4ek/5JU/V/4vYE3s98/Im3LCzAe6Fs1/yGpnaRtql13RLWfz9TwPXtVPQEmaQPgK8DMFc45jVTF9dJqhx8FTqg2H9NNUpeVb6nZqnGPxKx+6wO/l7QxUEmquFq1w9xw4GFJc7J5kuOB0ZLWzj7/GamKK8Dakp4l/QOupl7LzsC1kiqzc26MiOez3Rqr/ARYmg2dQSolfr2kbYFn0m6rLASOIe14aJY7P/5r1gQa8zFhs+bGQ1tmZtYg7pGYmVmDuEdiZmYN4kRiZmYN4kRiZmYN4kRiZmYN4kRiZmYN4kRiZmYN8v8Bspk12g0tv0gAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# test for the step size and the accuracy \n",
"accuracy2 = []\n",
"S_s2 = []\n",
"for Step_size in np.arange(0.0001, 0.006, 0.001):\n",
" Theta_N = log_reg(NX_Train, Y_train, Step_size, 10000)\n",
" Y_hat_N = predict_y(NX_Test, Theta_N)\n",
" accuracy2.append((Y_test == Y_hat_N).mean() * 100)\n",
" S_s2.append(float(Step_size))\n",
"# print(accuracy)\n",
" \n",
"plt.plot(S_s2, accuracy2, 'r-')\n",
"plt.xlabel('Step Size')\n",
"plt.ylabel('Accuracy (\\%)')"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"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": "3.7.1"
}
},
"nbformat": 4,
"nbformat_minor": 2
}