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import numpy as npfrom scipy.optimize import minimizeimport matplotlib.pyplot as pltimport pickle #Implement the function logisticObjVal def logisticObjVal(w, X, y):     # compute log-loss error (scalar) with respect    # to w (vector) for the given data X and y                                   # Inputs:    # w = d x 1    # X = N x d    # y = N x 1    # Output:    # error = scalar            if len(w.shape) == 1:        w = w[:,np.newaxis]    # IMPLEMENT THIS METHOD - REMOVE THE NEXT LINE    error = 0        return error #Implement the function logisticGradient def logisticGradient(w, X, y):     # compute the gradient of the log-loss error (vector) with respect    # to w (vector) for the given data X and y      #    # Inputs:    # w = d x 1    # X = N x d    # y = N x 1    # Output:    # error = d length gradient vector (not a d x 1 matrix)     if len(w.shape) == 1:        w = w[:,np.newaxis]    # IMPLEMENT THIS METHOD - REMOVE THE NEXT LINE    gradient = np.zeros((w.shape[0],))        return gradient #Implement the function predictLinearModel def predictLinearModel(w,Xtest):    # Inputs:    # w = d x 1    # Xtest = N x d    # Output:    # ypred = N x 1 vector of predictions     # IMPLEMENT THIS METHOD - REMOVE THE NEXT LINE    ypred = np.zeros([Xtest.shape[0],1])     return ypred #Implement the function evaluateLinearModel def evaluateLinearModel(w,Xtest,ytest):    # Inputs:    # w = d x 1    # Xtest = N x d    # ytest = N x 1    # Output:    # accuracy = scalar values    # precision = scalar values    # recall = scalar values    # f1 = scalar values        if len(w.shape) == 1:        w = w[:,np.newaxis]    # IMPLEMENT THIS METHOD - REMOVE THE NEXT LINE    acc = 0    precision = 0    recall = 0    f1 = 0        return acc, precision, recall, f1 Xtrain,ytrain, Xtest, ytest = pickle.load(open('sample.pickle','rb'))  Xtrain_i = np.concatenate((np.ones((Xtrain.shape[0],1)), Xtrain), axis=1)Xtest_i = np.concatenate((np.ones((Xtest.shape[0],1)), Xtest), axis=1) args = (Xtrain_i,ytrain)opts = {'maxiter' : 50}    # Preferred value.    w_init = np.zeros((Xtrain_i.shape[1],))soln = minimize(logisticObjVal, w_init, jac=logisticGradient, args=args,method='CG', options=opts)w = np.transpose(np.array(soln.x))w = np.reshape(w,[len(w),1])acc, pre, rec, f1 = evaluateLinearModel(w,Xtrain_i,ytrain)print('Logistic Regression results on train data - acc:%.2f, pre:%.2f, rec:%.2f, f1:%.2f'%(acc, pre, rec, f1))acc, pre, rec, f1 = evaluateLinearModel(w,Xtest_i,ytest)print('Logistic Regression results on test data - acc:%.2f, pre:%.2f, rec:%.2f, f1:%.2f'%(acc, pre, rec, f1)) def plotBoundaries(w,X,y):    # plotting boundaries     mn = np.min(X,axis=0)    mx = np.max(X,axis=0)    x1 = np.linspace(mn[1],mx[1],100)    x2 = np.linspace(mn[2],mx[2],100)    xx1,xx2 = np.meshgrid(x1,x2)    xx = np.zeros((x1.shape[0]*x2.shape[0],2))    xx[:,0] = xx1.ravel()    xx[:,1] = xx2.ravel()    xx_i = np.concatenate((np.ones((xx.shape[0],1)), xx), axis=1)    ypred = predictLinearModel(w,xx_i)    ax.contourf(x1,x2,ypred.reshape((x1.shape[0],x2.shape[0])),alpha=0.3,cmap='cool')    ax.scatter(X[:,1],X[:,2],c=y.flatten()) #Modify the code based on the comment Xtrain,ytrain, Xtest, ytest = pickle.load(open('sample.pickle','rb'))  Xtrain_i = np.concatenate((np.ones((Xtrain.shape[0],1)), Xtrain), axis=1)Xtest_i = np.concatenate((np.ones((Xtest.shape[0],1)), Xtest), axis=1) # Replace next line with code for learning w using the logistic regressionw_logistic = np.zeros((Xtrain_i.shape[1],1)) fig = plt.figure(figsize=(6,6)) ax = plt.subplot(1,1,1)plotBoundaries(w_logistic,Xtrain_i,ytrain)ax.set_title('Logistic Regression')

import numpy as npfrom scipy.optimize import minimizeimport matplotlib.pyplot as pltimport pickle #Implement the function logisticObjVal def logisticObjVal(w, X, y):     # compute log-loss error (scalar) with respect    # to w (vector) for the given data X and y                                   # Inputs:    # w = d x 1    # X = N x d    # y = N x 1    # Output:    # error = scalar            if len(w.shape) == 1:        w = w[:,np.newaxis]    # IMPLEMENT THIS METHOD - REMOVE THE NEXT LINE    error = 0        return error #Implement the function logisticGradient def logisticGradient(w, X, y):     # compute the gradient of the log-loss error (vector) with respect    # to w (vector) for the given data X and y      #    # Inputs:    # w = d x 1    # X = N x d    # y = N x 1    # Output:    # error = d length gradient vector (not a d x 1 matrix)     if len(w.shape) == 1:        w = w[:,np.newaxis]    # IMPLEMENT THIS METHOD - REMOVE THE NEXT LINE    gradient = np.zeros((w.shape[0],))        return gradient #Implement the function predictLinearModel def predictLinearModel(w,Xtest):    # Inputs:    # w = d x 1    # Xtest = N x d    # Output:    # ypred = N x 1 vector of predictions     # IMPLEMENT THIS METHOD - REMOVE THE NEXT LINE    ypred = np.zeros([Xtest.shape[0],1])     return ypred #Implement the function evaluateLinearModel def evaluateLinearModel(w,Xtest,ytest):    # Inputs:    # w = d x 1    # Xtest = N x d    # ytest = N x 1    # Output:    # accuracy = scalar values    # precision = scalar values    # recall = scalar values    # f1 = scalar values        if len(w.shape) == 1:        w = w[:,np.newaxis]    # IMPLEMENT THIS METHOD - REMOVE THE NEXT LINE    acc = 0    precision = 0    recall = 0    f1 = 0        return acc, precision, recall, f1 Xtrain,ytrain, Xtest, ytest = pickle.load(open('sample.pickle','rb'))  Xtrain_i = np.concatenate((np.ones((Xtrain.shape[0],1)), Xtrain), axis=1)Xtest_i = np.concatenate((np.ones((Xtest.shape[0],1)), Xtest), axis=1) args = (Xtrain_i,ytrain)opts = {'maxiter' : 50}    # Preferred value.    w_init = np.zeros((Xtrain_i.shape[1],))soln = minimize(logisticObjVal, w_init, jac=logisticGradient, args=args,method='CG', options=opts)w = np.transpose(np.array(soln.x))w = np.reshape(w,[len(w),1])acc, pre, rec, f1 = evaluateLinearModel(w,Xtrain_i,ytrain)print('Logistic Regression results on train data - acc:%.2f, pre:%.2f, rec:%.2f, f1:%.2f'%(acc, pre, rec, f1))acc, pre, rec, f1 = evaluateLinearModel(w,Xtest_i,ytest)print('Logistic Regression results on test data - acc:%.2f, pre:%.2f, rec:%.2f, f1:%.2f'%(acc, pre, rec, f1)) def plotBoundaries(w,X,y):    # plotting boundaries     mn = np.min(X,axis=0)    mx = np.max(X,axis=0)    x1 = np.linspace(mn[1],mx[1],100)    x2 = np.linspace(mn[2],mx[2],100)    xx1,xx2 = np.meshgrid(x1,x2)    xx = np.zeros((x1.shape[0]*x2.shape[0],2))    xx[:,0] = xx1.ravel()    xx[:,1] = xx2.ravel()    xx_i = np.concatenate((np.ones((xx.shape[0],1)), xx), axis=1)    ypred = predictLinearModel(w,xx_i)    ax.contourf(x1,x2,ypred.reshape((x1.shape[0],x2.shape[0])),alpha=0.3,cmap='cool')    ax.scatter(X[:,1],X[:,2],c=y.flatten()) #Modify the code based on the comment Xtrain,ytrain, Xtest, ytest = pickle.load(open('sample.pickle','rb'))  Xtrain_i = np.concatenate((np.ones((Xtrain.shape[0],1)), Xtrain), axis=1)Xtest_i = np.concatenate((np.ones((Xtest.shape[0],1)), Xtest), axis=1) # Replace next line with code for learning w using the logistic regressionw_logistic = np.zeros((Xtrain_i.shape[1],1)) fig = plt.figure(figsize=(6,6)) ax = plt.subplot(1,1,1)plotBoundaries(w_logistic,Xtrain_i,ytrain)ax.set_title('Logistic Regression')

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import numpy as np
from scipy.optimize import minimize
import matplotlib.pyplot as plt
import pickle

#Implement the function logisticObjVal

def logisticObjVal(w, X, y):

    # compute log-loss error (scalar) with respect
    # to w (vector) for the given data X and y                               
    # Inputs:
    # w = d x 1
    # X = N x d
    # y = N x 1
    # Output:
    # error = scalar
    
    
    if len(w.shape) == 1:
        w = w[:,np.newaxis]
    # IMPLEMENT THIS METHOD - REMOVE THE NEXT LINE
    error = 0
    
    return error

#Implement the function logisticGradient

def logisticGradient(w, X, y):

    # compute the gradient of the log-loss error (vector) with respect
    # to w (vector) for the given data X and y  
    #
    # Inputs:
    # w = d x 1
    # X = N x d
    # y = N x 1
    # Output:
    # error = d length gradient vector (not a d x 1 matrix)

    if len(w.shape) == 1:
        w = w[:,np.newaxis]
    # IMPLEMENT THIS METHOD - REMOVE THE NEXT LINE
    gradient = np.zeros((w.shape[0],))
    
    return gradient

#Implement the function predictLinearModel

def predictLinearModel(w,Xtest):
    # Inputs:
    # w = d x 1
    # Xtest = N x d
    # Output:
    # ypred = N x 1 vector of predictions

    # IMPLEMENT THIS METHOD - REMOVE THE NEXT LINE
    ypred = np.zeros([Xtest.shape[0],1])

    return ypred

#Implement the function evaluateLinearModel

def evaluateLinearModel(w,Xtest,ytest):
    # Inputs:
    # w = d x 1
    # Xtest = N x d
    # ytest = N x 1
    # Output:
    # accuracy = scalar values
    # precision = scalar values
    # recall = scalar values
    # f1 = scalar values
    
    if len(w.shape) == 1:
        w = w[:,np.newaxis]
    # IMPLEMENT THIS METHOD - REMOVE THE NEXT LINE
    acc = 0
    precision = 0
    recall = 0
    f1 = 0
    
    return acc, precision, recall, f1

Xtrain,ytrain, Xtest, ytest = pickle.load(open('sample.pickle','rb')) 

Xtrain_i = np.concatenate((np.ones((Xtrain.shape[0],1)), Xtrain), axis=1)
Xtest_i = np.concatenate((np.ones((Xtest.shape[0],1)), Xtest), axis=1)

args = (Xtrain_i,ytrain)
opts = {'maxiter' : 50}    # Preferred value.    
w_init = np.zeros((Xtrain_i.shape[1],))
soln = minimize(logisticObjVal, w_init, jac=logisticGradient, args=args,method='CG', options=opts)
w = np.transpose(np.array(soln.x))
w = np.reshape(w,[len(w),1])
acc, pre, rec, f1 = evaluateLinearModel(w,Xtrain_i,ytrain)
print('Logistic Regression results on train data - acc:%.2f, pre:%.2f, rec:%.2f, f1:%.2f'%(acc, pre, rec, f1))
acc, pre, rec, f1 = evaluateLinearModel(w,Xtest_i,ytest)
print('Logistic Regression results on test data - acc:%.2f, pre:%.2f, rec:%.2f, f1:%.2f'%(acc, pre, rec, f1))

def plotBoundaries(w,X,y):
    # plotting boundaries

    mn = np.min(X,axis=0)
    mx = np.max(X,axis=0)
    x1 = np.linspace(mn[1],mx[1],100)
    x2 = np.linspace(mn[2],mx[2],100)
    xx1,xx2 = np.meshgrid(x1,x2)
    xx = np.zeros((x1.shape[0]*x2.shape[0],2))
    xx[:,0] = xx1.ravel()
    xx[:,1] = xx2.ravel()
    xx_i = np.concatenate((np.ones((xx.shape[0],1)), xx), axis=1)
    ypred = predictLinearModel(w,xx_i)
    ax.contourf(x1,x2,ypred.reshape((x1.shape[0],x2.shape[0])),alpha=0.3,cmap='cool')
    ax.scatter(X[:,1],X[:,2],c=y.flatten())

#Modify the code based on the comment

Xtrain,ytrain, Xtest, ytest = pickle.load(open('sample.pickle','rb')) 

Xtrain_i = np.concatenate((np.ones((Xtrain.shape[0],1)), Xtrain), axis=1)
Xtest_i = np.concatenate((np.ones((Xtest.shape[0],1)), Xtest), axis=1)

# Replace next line with code for learning w using the logistic regression
w_logistic = np.zeros((Xtrain_i.shape[1],1))

fig = plt.figure(figsize=(6,6))


ax = plt.subplot(1,1,1)
plotBoundaries(w_logistic,Xtrain_i,ytrain)
ax.set_title('Logistic Regression')

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