Scikit-Learn 机器学习笔记 -- 线性回归、逻辑回归、softma

爱被打了一巴掌 2023-08-17 16:52 141阅读 0赞

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import numpy as np
    from matplotlib import pyplot as plt
    
    
    # 创建线性回归数据集
    def create_dataset():
        X = 2 * np.random.rand(100, 1)
        # 结果加上高斯噪声
        y = 4 + 3*X + np.random.randn(100, 1)
        return X, y
    
    
    # 线性回归解析法：使用正态方程求解，直接得到全局最优解
    def linear_regression_analysis(X, y):
        # 特征向量为参数b添加值为1的特征
        X_b = np.c_[np.ones((100, 1)), X]
        # 用正态方程解得全局最优解
        theta_best = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(y)
        print("线性回归解析解为：", theta_best)
        # 预测
        sample = np.array([[0], [2]])
        sample_b = np.c_[np.ones((2, 1)), sample]
        predict = sample_b.dot(theta_best)
        # print('解析解方程预测为：', predict)
        # 绘制线性回归模型图像
        plt.plot(sample, predict, 'r-')
        plt.plot(X, y, 'b.')
        plt.axis([0, 2, 0, 15])
        plt.show()
        return X_b
    
    
    # 使用sk-learn的线性回归模型，默认使用解析法
    def linear_regression_sk(X, y):
        from sklearn.linear_model import LinearRegression
        # 创建线性回归模型实例
        lin_reg = LinearRegression()
        lin_reg.fit(X, y)
        print('sk-learn线性回归解析解：', 'b：', lin_reg.intercept_, 'w：', lin_reg.coef_)
    
    
    # 线性回归批量梯度下降法（batch gradient descent）
    def linear_regression_batch_gd(X_b, y):
        # 学习率不变、迭代次数和样本数
        learning_rate = 0.1
        max_iterations = 1000
        m = 100
        # 随机初始值
        theta = np.random.randn(2, 1)
        # 开始迭代
        for n in range(max_iterations):
            gradients = 2/m * X_b.T.dot(X_b.dot(theta)-y)
            theta = theta - learning_rate*gradients
        print('线性回归批量梯度下降法解：', theta)
    
    
    # 线性回归随机梯度下降法（stochastic gradient descent）
    def linear_regression_stochastic_gd(X_b, y):
        # epoch次数，样本数
        n_epochs = 50
        m = 100
        theta = np.random.randn(2, 1)
        for epoch in range(n_epochs):
            for i in range(m):
                random_index = np.random.randint(m)
                xi = X_b[random_index:random_index+1]
                yi = y[random_index:random_index+1]
                gradients = 2 * xi.T.dot(xi.dot(theta) - yi)
                learning_rate = 1.0/(epoch*m + i + 10)
                theta = theta - learning_rate*gradients
        print('线性回归随机梯度下降法解：', theta)
    
    
    # sk-learn 线性回归随机梯度下降
    def linear_regression_stochastic_gd_sk(X, y):
        from sklearn.linear_model import SGDRegressor
        sgd_reg = SGDRegressor(n_iter=50, penalty=None, eta0=0.1)
        sgd_reg.fit(X, y.ravel())
        print('sk-learn线性回归随机梯度下降法解：',  'b：', sgd_reg.intercept_, 'w：', sgd_reg.coef_)
    
    
    # 创建多项式回归数据集
    def create_dataset_poly():
        m = 100
        X1 = 6 * np.random.rand(m, 1) - 3
        y1 = 0.5 * X1 ** 2 + X1 + 2 + np.random.randn(m, 1)
        return X1, y1
    
    
    # 多项式回归
    def polynomial_regression(X, y):
        # 添加二次特征
        from sklearn.preprocessing import PolynomialFeatures
        from sklearn.linear_model import LinearRegression
        poly_features = PolynomialFeatures(degree=2, include_bias=False)
        X_poly = poly_features.fit_transform(X)
        lin_reg_poly = LinearRegression()
        lin_reg_poly.fit(X_poly, y)
        print('多项式回归解：', 'b：', lin_reg_poly.intercept_, 'w：', lin_reg_poly.coef_)
        return lin_reg_poly
    
    
    # 绘制关于训练集规模的学习曲线
    def plot_learning_curves(model, X, y):
        from sklearn.metrics import mean_squared_error
        from sklearn.model_selection import train_test_split
        X_train, X_val, y_train, y_val = train_test_split(X, y, test_size=0.2)
        train_errors, val_errors = [], []
        for m in range(1, len(X_train)):
            model.fit(X_train[:m], y_train[:m])
            y_train_predict = model.predict(X_train[:m])
            y_val_predict = model.predict(X_val)
            train_errors.append(mean_squared_error(y_train_predict, y_train[:m]))
            val_errors.append(mean_squared_error(y_val_predict, y_val))
        plt.plot(np.sqrt(train_errors), "r-+", linewidth=2, label="train")
        plt.plot(np.sqrt(val_errors), "b-", linewidth=3, label="val")
        plt.show()
    
    
    # 岭回归，l2正则化，封闭方程求解
    def ridge_regression_analysis(X, y):
        from sklearn.linear_model import Ridge
        ridge_reg = Ridge(alpha=1, solver="cholesky")
        ridge_reg.fit(X, y)
        print('岭回归解：', 'b：', ridge_reg.intercept_, 'w：', ridge_reg.coef_)
    
    
    # Lasso 回归，l2正则化，封闭方程求解
    def lasso_regression_analysis(X, y):
        from sklearn.linear_model import Lasso
        lasso_reg = Lasso(alpha=0.1)
        lasso_reg.fit(X, y)
        print('Lasso 回归解：', 'b：', lasso_reg.intercept_, 'w：', lasso_reg.coef_)
    
    
    # l2,l1正则化，梯度下降求解
    def regularization_regression_gd(X, y):
        from sklearn.linear_model import SGDRegressor
        # l1正则化把 penalty="l2" 改为 penalty="l1"
        sgd_reg = SGDRegressor(penalty="l2")
        sgd_reg.fit(X, y.ravel())
        print('l2梯度下降法解：', 'b：', sgd_reg.intercept_, 'w：', sgd_reg.coef_)
    
    
    # 弹性网路正则化，即l1、l2混合正则化
    def elasticnet_regression_gd(X, y):
        from sklearn.linear_model import ElasticNet
        # l1_ratio 指的就是混合率, 即l1正则化占的比例
        elastic_net = ElasticNet(alpha=0.1, l1_ratio=0.5)
        elastic_net.fit(X, y)
        print('弹性网络解：', 'b：', elastic_net.intercept_, 'w：', elastic_net.coef_)
    
    
    # 早期停止法（Early Stopping）
    def early_stoping(X, y):
        from sklearn.base import clone
        from sklearn.linear_model import SGDRegressor
        from sklearn.metrics import mean_squared_error
        from sklearn.model_selection import train_test_split
        # 当warm_start=True时，调用fit()方法后，训练会从停下来的地方继续，而不是从头重新开始。
        sgd_reg = SGDRegressor(max_iter=1, warm_start=True, penalty=None, learning_rate="constant", eta0=0.0005)
        X_train, X_val, y_train, y_val = train_test_split(X, y, test_size=0.2)
        minimum_val_error = float("inf")
        best_epoch = None
        best_model = None
        for epoch in range(1000):
            sgd_reg.fit(X_train,  y_train.ravel())
            y_val_predict = sgd_reg.predict(X_val)
            val_error = mean_squared_error(y_val_predict, y_val)
            if val_error < minimum_val_error:
                minimum_val_error = val_error
                best_epoch = epoch
                best_model = clone(sgd_reg)
        print('stopping in:', best_epoch)
    
    
    # 加载鸢尾花数据集
    def load_dataset_flower():
        from sklearn import datasets
        iris = datasets.load_iris()
        # X_f = iris['data']
        # y_f = iris['target']
        # print('加载鸢尾花数据集成功：', iris)
        return iris
    
    
    # logistic 回归
    def logistic_classify(iris):
        from sklearn.linear_model import LogisticRegression
        X = iris["data"][:, 3:]  # petal width
        y = (iris["target"] == 2).astype(np.int)
        log_reg = LogisticRegression()
        log_reg.fit(X, y)
        # 绘图
        X_new = np.linspace(0, 3, 1000).reshape(-1, 1)
        y_proba = log_reg.predict_proba(X_new)
        plt.plot(X_new, y_proba[:, 1], "g-", label="Iris-Virginica")
        plt.plot(X_new, y_proba[:, 0], "b--", label="Not Iris-Virginica")
        plt.show()
    
    
    # softmax 回归多分类
    def softmax_classify(iris):
        from sklearn.linear_model import LogisticRegression
        # 划分数据集
        X = iris["data"][:, (2, 3)]  # petal length, petal width
        y = iris["target"]
        # 创建 softmax 回归实例
        softmax_reg = LogisticRegression(multi_class="multinomial", solver="lbfgs", C=10)
        softmax_reg.fit(X, y)
        # 预测
        predict = softmax_reg.predict([[5, 2]])
        predict_pro = softmax_reg.predict_proba([[5, 2]])
        print('softmax回归预测为：', predict, '各类概率为', predict_pro)
    
    
    if __name__ == '__main__':
        # 获得线性回归数据集
        X, y = create_dataset()
        # 线性回归解析法
        # X_b = linear_regression_analysis(X, y)
        # sk-learn线性回归解
        # linear_regression_sk(X, y)
        # 线性回归批量梯度下降法
        # linear_regression_batch_gd(X_b, y)
        # 线性回归随机梯度下降法
        # linear_regression_stochastic_gd(X_b, y)
        # sk-learn线性回归随机梯度下降法
        # linear_regression_stochastic_gd_sk(X, y)
        # 获得多项式回归数据集
        # X1, y1 = create_dataset_poly()
        # 多项式回归解
        # lin_reg_poly = polynomial_regression(X1, y1)
        # 获得关于训练集规模的学习曲线
        # plot_learning_curves(lin_reg_poly, X1, y1)
        # 岭回归，l2正则化
        # ridge_regression_analysis(X, y)
        # lasso回归，l1正则化
        # lasso_regression_analysis(X, y)
        # 梯度下降法的正则化
        # regularization_regression_gd(X, y)
        # 弹性网络
        # elasticnet_regression_gd(X, y)
        # 早期停止
        # early_stoping(X1, y1)
        # 加载花的数据集
        iris = load_dataset_flower()
        # logistic 回归二分类
        logistic_classify(iris)
        # softmax 多分类
        softmax_classify(iris)

本文链接： [https://blog.csdn.net/Wang\_Jiankun/article/details/81114716][https_blog.csdn.net_Wang_Jiankun_article_details_81114716]

转载于:https://www.cnblogs.com/lvdongjie/p/11523876.html

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[https_blog.csdn.net_Wang_Jiankun_article_details_81114716]: https://blog.csdn.net/Wang_Jiankun/article/details/81114716