linear_regression.py

## linear_regression.py
'''
Linear Regression From First Principles
Author: Gaurav Menghani (gaurav.menghani@gmail.com)
'''

import numpy as np
import matplotlib.pyplot as plt

def linear_sum(X, W, b):
    return X.dot(W) + b

def data_gen(num_rows, num_feats, op_gen_fn=linear_sum):
    data = {}
    W = 0.1 * np.random.randn(num_feats)
    b = 0.1 * np.random.randn()
    data['X'] = np.random.randn(num_rows, num_feats)
    data['y'] = op_gen_fn(data['X'], W, b)
    return data

class LinearRegression(object):
    def __init__(self):
        self.W = None
        self.b = 0

    def init_matrix(self, X):
        self.W = 0.1 * np.random.randn(X.shape[1])
        self.b = 0.1 * np.random.randn()

    def predict(self, X):
        if self.W is None:
            self.init_matrix(X)

        return X.dot(self.W) + self.b

    def diff(self, pred, y):
        return pred-y

    def l1_loss(self, pred, y):
        return reduce(lambda a,b: a+b, self.diff(pred, y)) * 1.0 / len(y)

    def l2_loss(self, pred, y):
        return reduce(lambda a,b: a+b*b, self.diff(pred, y)) * 1.0 / len(y)

    def loss(self, pred, y):
        return self.l2_loss(pred, y)

    def train(self, data, iters, lr):
        X = data['X']
        y = data['y']

        orig_pred = self.predict(X)
        orig_l1 = self.l1_loss(orig_pred, y)
        orig_l2 = self.l2_loss(orig_pred, y)

        print_every = 50
        l1 = orig_l1
        l2 = orig_l2

        l1_losses = []
        l2_losses = []
        l1_losses.append(l1)
        l2_losses.append(l2)

        for it in range(iters):
            pred = self.predict(X)

            s1 = (pred - y)
            s2 = np.multiply(X, np.repeat(s1, X.shape[1])\
                    .reshape(X.shape[0], X.shape[1]))
            wGrad = np.sum(s2, axis=0) / X.shape[0]
            bGrad = np.sum(s1) * 1.0 / X.shape[0]

            wDelta = -lr * wGrad
            bDelta = -lr * bGrad
            self.W += wDelta
            self.b += bDelta

            l1 = self.l1_loss(pred, y)
            l2 = self.l2_loss(pred, y)

            l1_losses.append(l1)
            l2_losses.append(l2)

            if it % print_every == 0:
                print 'Iteration: ' + str(it)
                print 'L1 loss: %Lf, L2 loss: %Lf' % (l1, l2)
                print '---'

        print '\n===='
        print 'Original L1 loss: %Lf, L2 loss: %Lf ' % (orig_l1, orig_l2)
        print 'Final L1 loss: %Lf, L2 loss: %Lf' % (l1, l2)
        print 'Estimated Params: '
        print '- b: ', self.b
        print '- W: ', self.W
        print '====\n'

        fig = plt.figure()
        ax = fig.add_subplot(111)
        ax.set_title('Linear Regression Over %d Variables' % X.shape[1])
        ax.set_xlabel('Iterations')
        ax.set_ylabel('L2 Loss')
        plt.gca().set_ylim(ymin=0)
        plt.plot(l2_losses, label='lr')
        plt.show()

np.random.seed(2)
data = data_gen(100, 5)

# Persist training data
data_file = open('lin_reg_data', 'w')
for xd,yd in zip(data['X'], data['y']):
    line = str(yd) + ',' + ','.join(str(x) for x in xd) + "\n"
    data_file.write(line)
data_file.close()

regression = LinearRegression()
predictions = regression.predict(data['X'])
loss = regression.loss(predictions, data['y'])
regression.train(data, iters=1000, lr=0.01)