梯度下降法(BGD)

# coding-utf-8
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt


class LR:
    def __init__(self, data, learning_rate=0.001, iter_max=10000, batch_size=2):
        self.data = data
        self.learning_rate = learning_rate
        self.iter_max = iter_max
        self.batch_size = batch_size
        self.process_data()

    # 数据标准化 
    def standard_scaler(self, data):
        data1 = data[:, :-1]
        mean = np.mean(data1, axis=0)
        std = np.std(data1, axis=0)
        data1 = (data1 - mean) / std
        return np.hstack((data1, data[:, -1:]))

    def process_data(self):
        data = np.array(self.data)
        data = self.standard_scaler(data)
        one = np.ones((data.shape[0], 1))
        self.data = np.hstack((one, data))
        self.m = self.data.shape[0]  # 样本总数量
        self.n = self.data.shape[1] - 1  # 特征总数量

    def model(self):
        return np.dot(self.data[:, :-1], self.theta)

    def mse(self, predict, y):
        return np.sum((predict - y) ** 2) / len(y)

    def cal_grad(self, predict, y):
        grad = np.ones(self.theta.shape)
        for i in range(len(grad)):
            grad[i] = np.mean((predict - y) * self.data[:, i])
        return grad

    @staticmethod
    def draw(list_data):
        plt.plot(range(len(list_data)), list_data)
        plt.show()

    def train(self):
        loss_list = []
        n = 1
        # 1、初始化theta 
        self.theta = np.ones((self.n, 1))
        predict = self.model()
        # 2、计算误差
        loss = self.mse(predict, self.data[:, -1:])
        loss_list.append(loss)
        while True:
            # 3、求梯度
            grad = self.cal_grad(predict, self.data[:, -1:])
            # 4、更新theta
            self.theta = self.theta - self.learning_rate * grad
            # 5、计算误差
            predict = self.model()
            loss = self.mse(predict, self.data[:, -1:])
            loss_list.append(loss)
            # if 判断停止条件 满足则跳出训练
            if n > self.iter_max:
                break
            n += 1
        self.draw(loss_list)


if __name__ == "__main__":
    data = pd.read_excel('C:/Users/jiedada/Desktop/python/回归/lr.xlsx')
    lr = LR(data)
    lr.train()