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

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。

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()