Ndtyjky

I have already did the training for the data but I am not sure how to do the rest. I just need someone to explain how I should proceed?

Implement a perceptron for logistric regression. For your training data, generate 2000 training instances in two sets of random data points (1000 in each) from multi-variate normal
distribution with:

µ1 = [1, 0]

µ2 = [0, 1.5] 

Σ1 = [[1, 0.75], [0.75, 1]]

Σ2 = [[1, 0.75], [0.75, 1]] 

and label them 0 and 1. Generate testing data in the same manner but include 500 instances for each class,
i.e., 1000 in total. Use sigmoid function for your activation function and cross entropy for your objective function. You will implement a logistic regression for the following questions. Initialize the starting weight as w = [1, 1, 1]. During training, stop your loop when the objective function (i.e., cross entropy) does not decrease any more (below certain threshold) or when the gradient is close to 0 or the iteration reaches 10000.
Set your thresholds properly so that the iteration doesn’t reach 10000 for all the learning rate that you will be using.

This is the code I have already written:

import numpy as np

def sigmoid(z):

   return 1/(1/np.exp(-z))



#def cross_entropy():



mu1 = [1,0]

mu2 = [0,1.5]

sigma1 = [[1,0.75],[0.75,1]]

sigma2 = [[1,0.75],[0.75,1]]

zero =np.append(np.random.multivariate_normal(mu1,sigma1,1000),np.zeros((1000,1)),axis=1)

one = np.append(np.random.multivariate_normal(mu2,sigma2,1000),np.ones((1000,1)),axis=1)

s0 = np.append(np.random.multivariate_normal(mu1,sigma1,500),np.zeros((500,1)),axis=1)

s1 = np.append(np.random.multivariate_normal(mu2,sigma2,500),np.ones((500,1)),axis=1)



w = [1,1,1]