线性回归手动实现代码

青旅半醒 2022-02-02 13:06 252阅读 0赞

import numpy as np
    import matplotlib.pyplot as plt
    from sklearn import datasets, linear_model
    
    
    def plot_line(x, y, y_hat,line_color='blue'):
        # Plot outputs
        plt.scatter(x, y,  color='black')
        plt.plot(x, y_hat, color=line_color,
                 linewidth=3)
        plt.xticks(())
        plt.yticks(())
    
        plt.show()
    
    
    def linear_grad_func(theta, x, y):
        # np.r_是按列连接两个矩阵，就是把两矩阵上下相加，要求列数相等。
        # np.c_是按行连接两个矩阵，就是把两矩阵左右相加，要求行数相等。
        # compute gradient
        grad = np.dot((linear_val_func(theta, x) - y).T, np.c_[np.ones(x.shape[0]), x])
        grad = grad / x.shape[0]
    
        return grad
    
    
    def linear_val_func(theta, x):
        # forwarding
        return np.dot(np.c_[np.ones(x.shape[0]), x], theta.T)
    
    
    def linear_cost_func(theta, x, y):
        # compute cost (loss)
        y_hat = linear_val_func(theta, x)
        cost = np.dot(y_hat.T, y)
    
        return cost
    
    
    def linear_grad_desc(theta, X_train, Y_train, lr=0.1, max_iter=10000, converge_change=.001):
    
        cost_iter = []
        cost = linear_cost_func(theta, X_train, Y_train)
        cost_iter.append([0, cost])
        cost_change = 1
        i = 1
        while cost_change > converge_change and i< max_iter:
            pre_cost = cost
            # compute gradient
            grad = linear_grad_func(theta, X_train, Y_train)
            theta -= lr * grad
            cost = linear_cost_func(theta, X_train, Y_train)
            cost_iter.append([i, cost])
            cost_change = abs(cost - pre_cost)
            i += 1
    
        return theta, cost_iter
    
    
    def linear_regression():
        # load dataset
        dataset = datasets.load_diabetes()
        # Select only 2 dims
        X = dataset.data[:, 2]
        Y = dataset.target
    
        # split dataset into training and testing
        X_train = X[:-20, None]
        X_test = X[-20:, None]
    
        Y_train = Y[:-20, None]
        Y_test = Y[-20:, None]
    
    
        # Linear regression
        theta = np.random.rand(1, X_train.shape[1]+1)
        fitted_theta, cost_iter = linear_grad_desc(theta, X_train, Y_train, lr=0.1, max_iter=50000)
    
        print('Coefficients: {}'.format(fitted_theta[0,-1]))
        print('Intercept: {}'.format(fitted_theta[0,-2]))
        print('MSE: {}'.format(np.sum((linear_val_func(fitted_theta, X_test) - Y_test)**2) / Y_test.shape[0]))
    
        plot_line(X_test, Y_test, linear_val_func(fitted_theta, X_test))
    
    
    def sklearn_linear_regression():
        # load dataset
        dataset = datasets.load_diabetes()
        # Select only 2 dims
        X = dataset.data[:, 2]
        Y = dataset.target
    
        # split dataset into training and testing
        X_train = X[:-20, None]
        X_test = X[-20:, None]
    
        Y_train = Y[:-20, None]
        Y_test = Y[-20:, None]
    
        # Linear regression
        regressor = linear_model.LinearRegression()
        regressor.fit(X_train, Y_train)
        print('Coefficients: {}'.format(regressor.coef_))
        print('Intercept: {}'.format(regressor.intercept_))
        print('MSE:{}'.format(np.mean((regressor.predict(X_test) - Y_test) ** 2)))
    
        plot_line(X_test, Y_test, regressor.predict(X_test),line_color='red')
    
    
    def main():
        print('Class 1 Linear Regression Example')
        linear_regression()
    
        print ('')
    
        print('sklearn Linear Regression Example')
        sklearn_linear_regression()
    
    
    if __name__ == "__main__":
        main()