Binary Logistic Regression

#blog post https://oriamathematics.wordpress.com/2016/08/12/binary-classification-with-logistic-regression/
import numpy as np
import matplotlib.pyplot as plt

def predict(X, W):
    return 1/(1+np.exp(-np.dot(X, W)))

def logLikelihood(X, Y, W):
    m = X.shape[0]
    predictions = predict(X, W)
    onesVector = np.ones((m, 1))
    return np.dot(Y.T, np.log(predictions)) + np.dot((onesVector - Y).T, np.log(onesVector - predictions + np.min(predictions)/(100*m)))

def gradient(X, Y, W):
    return np.dot(X.T, Y - predict(X, W))

def successRate(X, Y, W):
    m = Y.shape[0]
    predictions = predict(X, W) > 0.5
    correct = (Y == predictions)
    return 100 * np.sum(correct)/float(correct.shape[0])

trX = np.load("binaryMnistTrainX.npy")
trY = np.load("binaryMnistTrainY.npy")
teX = np.load("binaryMnistTestX.npy")
teY = np.load("binaryMnistTestY.npy")

m, n = trX.shape
trX = np.concatenate((trX, np.ones((m, 1))),axis=1)
teX = np.concatenate((teX, np.ones((teX.shape[0], 1))),axis=1)
W = np.random.rand(n+1, 1)

learningRate = 0.00001
numIter = 100

likelihoodArray = np.zeros((numIter, 1))

for i in range(0, numIter):
    W = W + learningRate * gradient(trX, trY, W)
    likelihoodArray[i, 0] = logLikelihood(trX, trY, W)

print("train success rate is %lf" %(successRate(trX, trY, W)))
print("test success rate is %lf" %(successRate(teX, teY, W)))

plt.plot(likelihoodArray)
plt.xlabel("Iteration")
h = plt.ylabel("Log-Likelihood")
h.set_rotation(0)
plt.show()