ミニバッチ勾配降下法

mini_batch_gradient_descent.py

# -*- coding: utf-8 -*-

import re
import urllib2
import random
import numpy


def _batch_indexes(indexes, batch_size):
    for i in range(0, len(indexes), batch_size):
        yield indexes[i:i+batch_size]


def mini_batch_gradient_descent(X, y, initial_theta, alpha, num_iters=1500,
                                batch_size=100):
    u"""データセットに対してミニバッチ勾配降下法を実行し
    目的関数を最小化するθを求める。

    :param numpy.ndarray X: 説明変数Xのベクトル
    :param numpy.ndarray y: 結果Yのベクトル
    :param numpy.ndarray initial_theta: θの初期値
    :param float alpha: 学習率
    :param int num_iters: 繰り返し回数
    :param int batch_size: バッチサイズ
    :return: 目的関数を最小化するθ
    """
    theta = numpy.copy(initial_theta)
    xp = numpy.copy(X)
    xp = numpy.insert(xp, 0, 1, axis=1)
    for i in xrange(num_iters):
        indexes = list(range(len(xp)))
        random.shuffle(indexes)

        for cur_indexes in _batch_indexes(indexes, batch_size):
            _xp = xp[cur_indexes, :]
            _y = y[cur_indexes, :]
            grad = (1.0/_xp.shape[0]) * numpy.sum((_xp.dot(theta) - _y)*_xp,
                                                  axis=0,
                                                  keepdims=True)
            theta = theta - (alpha * grad).T
    return theta


if __name__ == '__main__':
    datasrc = 'https://archive.ics.uci.edu/ml/machine-learning-databases/housing/housing.data'
    data = urllib2.urlopen(datasrc).read().replace('\\n', '').splitlines()
    data = numpy.array([[float(v) for v in re.split(" +", row.strip())]
                       for row in data])
    X = data[:, :-1]
    Y = data[:, -1:]
    initial_theta = numpy.zeros((data.shape[1], 1))
    alpha = 0.01
    num_iters = 1500

    # Normalize
    X = (X - numpy.mean(X, axis=0)) / numpy.std(X, axis=0)

    print mini_batch_gradient_descent(X, Y, initial_theta, alpha, num_iters)