机器学习之linear_model(普通最小二乘法手写+sklearn实现+评价指标)

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y=wi*xi+b，基于最小二乘法的线性回归：寻找参数w和b，使得w和b对x_test_data的预测值y_pred_data与真实的回归目标y_test_data之间的均方误差最小。

公式推导：

基于最小二乘法构造linear_model有5个步骤：
1、导包。

from sklearn import linear_model
import numpy as np
import matplotlib.pyplot as plt
from sklearn.metrics import mean_squared_error,r2_score,mean_absolute_error

sklearn中有专门的线性模型包linear_model，numpy用于生成数据，matplotlib用于画图，另外导入MSE，R_Square和MAE三个评价指标。
2、构造数据集。可以自动生成数据，也可以寻找现有数据，以下数据是作业中的数据，样本数据只有一个特征。
3、训练模型。
4、输出系数w和截距b并对测试集进行预测。
5、作图。

完整代码：

import pandas as pd
import matplotlib.pyplot as plt
from sklearn import linear_model
import numpy as np
from sklearn.metrics import mean_squared_error, r2_score, mean_absolute_error


def load_data():
    data = pd.read_csv('Salary_Data.csv', encoding='gbk')
    data = data.values.tolist()
    train_x = []
    train_y = []
    test_x = []
    test_y = []
    # 前一半作为训练集，后一半作为测试集
    for i in range(len(data)):
        if i < len(data) / 2:
            train_x.append(data[i][0])
            train_y.append(data[i][1])
        else:
            test_x.append(data[i][0])
            test_y.append(data[i][1])
    return train_x, train_y, test_x, test_y


def model():
    print('手写：')
    train_x, train_y, test_x, test_y = load_data()
    # 最小二乘法得到参数
    sum = 0.0
    sum_square = 0.0
    sum_2 = 0.0
    sum_b = 0.0
    for i in range(len(train_x)):
        sum = sum + train_x[i]
        sum_square = sum_square + train_x[i] ** 2
    ave_x = sum / len(train_x)
    for i in range(len(train_x)):
        sum_2 = sum_2 + (train_y[i] * (train_x[i] - ave_x))
    w = sum_2 / (sum_square - sum ** 2 / len(train_x))
    for i in range(len(train_x)):
        sum_b = sum_b + (train_y[i] - w * train_x[i])
    b = sum_b / len(train_x)
    print('w=', w, 'b=', b)
    # 测试
    pred_y = []
    for i in range(len(test_x)):
        pred_y.append(w * test_x[i] + b)
    # 计算MSE,MAE,r2_score
    sum_mse = 0.0
    sum_mae = 0.0
    sum1 = 0.0
    sum2 = 0.0
    for i in range(len(pred_y)):
        sum_mae = sum_mae + np.abs(pred_y[i] - test_y[i])
        sum_mse = sum_mse + (pred_y[i] - test_y[i]) ** 2
    sum_y = 0.0
    for i in range(len(test_y)):
        sum_y = sum_y + test_y[i]
    ave_y = sum_y / len(test_y)
    for i in range(len(pred_y)):
        sum1 = sum1 + (pred_y[i] - test_y[i]) ** 2
        sum2 = sum2 + (ave_y - test_y[i]) ** 2
    print('MSE:', sum_mse / len(pred_y))
    print('MAE:', sum_mae / len(pred_y))
    print('R2_Squared:', 1 - sum1 / sum2)
    # 显示
    plt.scatter(test_x, test_y, color='black')
    plt.plot(test_x, pred_y, color='blue', linewidth=3)
    plt.show()
    print('\n')


# 调包
def sklearn_linearmodel():
    print('调包：')
    train_x, train_y, test_x, test_y = load_data()
    train_x = np.array(train_x).reshape(-1, 1)
    train_y = np.array(train_y).reshape(-1, 1)
    test_x = np.array(test_x).reshape(-1, 1)
    test_y = np.array(test_y).reshape(-1, 1)
    # 训练+测试
    lr = linear_model.LinearRegression()
    lr.fit(train_x, train_y)
    y_pred = lr.predict(test_x)

    # 输出系数和截距
    print('w:', lr.coef_, 'b:', lr.intercept_)
    # 输出评价指标
    print('MSE:', mean_squared_error(test_y, y_pred))
    print('MAE:', mean_absolute_error(test_y, y_pred))
    print('R2_Squared:', r2_score(test_y, y_pred))

    # 显示
    plt.scatter(test_x, test_y, color='black')
    plt.plot(test_x, y_pred, color='blue', linewidth=3)
    plt.show()


if __name__ == '__main__':
    model()
    sklearn_linearmodel()