线性回归参数估计--最小二乘法与梯度下降法Python实现

在上一篇 线性回归参数估计–最小二乘法与梯度下降法完成算法学习后，在这篇博客中贴出Python实现的代码。
这里使用的数据集来自Computer Hardware Data Set 。
数据集下载地址

实现代码

#!/usr/bin/python3
# -*- coding: utf-8 -*-
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd


class linear_classifier(object):
    """docstring for  linear_classifier"""

    def __init__(self, train_set, label_set):
        self.__train_set = train_set
        self.__target_mat = np.mat(label_set).T
        self.__thet = None
        self.__errores = []

    def fit(self, algorithm='gradient_descent', iterations=100000, alpha=0.03):
        if algorithm == 'least_squares':
            self.__least_squares()
        elif algorithm == 'gradient_descent':
            self.__gradient_descent(iterations, alpha)

    def __gradient_descent(self, iterations=100000, alpha=0.03):
        # gradient_descent
        m, n = np.shape(self.__train_set)
        data = np.ones((m, n + 1))
        data[:, 1:] = self.__train_set
        data = np.mat(data, dtype=np.float32)
        self.__thet = np.random.rand(n + 1, 1)
        for i in range(iterations):
            h = np.dot(data, self.__thet)
            err = h - self.__target_mat
            if i % (iterations / 100) == 0:
                self.__errores.append(np.dot(err.T, err))
            delta_thet = (1.0 / m) * alpha * np.dot(data.T, err)
            self.__thet = self.__thet - delta_thet
        pass

    def __least_squares(self):
        '''
        w=(X.T*X).I*X.T*y
        '''
        m, n = np.shape(self.__train_set)
        data = np.ones((m, n + 1))
        data[:, 1:] = self.__train_set
        data = np.mat(data, dtype=np.float32)
        self.__thet = np.dot(
            np.dot(np.dot(data.T, data).I, data.T), self.__target_mat)
        pass

    def classifier(self, item):
        n = len(item)
        tmp = np.ones((1, n + 1))
        tmp[0, 1:] = item
        return np.dot(tmp, self.__thet)

    def get_thet(self):
        return self.__thet

    def get_errores(self):
        return self.__errores


if __name__ == '__main__':
    data = pd.read_csv('../dataset/machine/machine.data')
    _xdata = data['PRP'].copy()
    collist = ['MYCT', 'MMIN', 'MMAX', 'CACH', 'CHMIN', 'CHMAX', 'PRP']
    for col in collist:
        data[col] = data[col].apply(lambda x: float(x))
        min = data[col].min()
        max = data[col].max()
        # min_max_normalize
        data[col] = data[col].apply(lambda x: (
            x - min) / (max - min))
    train_set = data[collist[:-1]].values
    tartget = data[collist[-1]].values
    classifier1 = linear_classifier(
        train_set, tartget)
    classifier1.fit(algorithm='least_squares')
    print('--------least_squares--------')
    print(classifier1.get_thet())
    classifier2 = linear_classifier(
        train_set, tartget)
    classifier2.fit(algorithm='gradient_descent',
                    iterations=100000, alpha=0.03)
    print('-------gradient_descent------')
    print(classifier2.get_thet())
    y = np.array(classifier2.get_errores()).reshape(1, 100)[0]
    x = np.arange(100)
    plt.plot(x, y)
    plt.show()

运行结果：

误差收敛图

模型参数输出

--------least_squares--------
    [[-0.05221016]
     [ 0.06333259]
     [ 0.42690573]
     [ 0.31137693]
     [ 0.14353076]
     [-0.0122879 ]
     [ 0.22807131]]
-------gradient_descent------
    [[-0.05220982]
     [ 0.06333198]
     [ 0.42691449]
     [ 0.31137109]
     [ 0.14352949]
     [-0.01229022]
     [ 0.22807503]]

可以看到，最小二乘法与梯度下降法得到的模型参数是吻合的。