logistic.py

import sys
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

data = pd.read_csv('data/iris.csv', delimiter=',', header=0)

data['y'] = 0
data.loc[data['species'] == 'virginica', 'y'] = 1

X = np.matrix(data[['sepal_length','sepal_width','petal_length','petal_width']])

y = np.matrix(data['y']).T

def scale(data):
    means = np.mean(data, 0)
    stds = np.std(data, 0)

    return (data-means)/stds

def logistic(z):
    return 1./(1+np.exp(-z))

def plot_boundary(Zs, Hs, y):
    data_fit = np.concatenate((Zs, Hs), axis=1)
    data_fit.sort(axis = 0)

    z = np.linspace(Zs.min(), Zs.max(), 100)

    plt.plot(z, logistic(z), 'r-', label='Theory')
    plt.plot(Zs, Hs, 'X', label='empirical')
    plt.plot(Zs, y, '*', label = 'data')
    plt.xlabel('z')
    plt.ylabel('h(z)')
    plt.title('Logistic Regression')
    plt.legend()
    #plt.show()

def plot_points(data, features, weights, label='y'):
    plt.plot(data[features[0]][data[label]==0], data[features[1]][data[label]==0], '*', label='y=0')
    plt.plot(data[features[0]][data[label]==1], data[features[1]][data[label]==1], '+', label='y=1')

    plt.xlabel(features[0])
    plt.ylabel(features[1])
    plt.legend()
    #plt.show()

alpha = 0.5
M, N = X.shape

X = np.concatenate((np.ones((M, 1)), X), axis=1)

epsilon = 0.12

weights = 2*np.random.rand(N+1, 1)*epsilon - epsilon
count = 0

oldJ = 0
err = 1

Js = []

while err > 1e-3:
    Zs = np.dot(X, weights)
    Hs = logistic(Zs)
    deltas = alpha/M*np.dot(X.T, (Hs-y))

    count += 1
    weights -= deltas

    J = -1/M*np.dot(y.T, np.log(Hs)) - np.dot(1-y.T, np.log(1-Hs))
    Js.append(float(J))
    err = np.abs(oldJ-J)
    oldJ = J

    print(count, J, err, weights.flatten())