常见的机器学习算法（二）逻辑回归

偏执的太偏执、 2023-02-12 04:28 50阅读 0赞

与线性回归不同，Logistic 回归没有封闭解。但由于损失函数是凸函数，因此我们可以使用梯度下降法来训练模型。

我们希望模型得到的目标值概率落在 0 到 1 之间。因此在训练期间，我们希望调整参数，使得模型较大的输出值对应正标签(真实标签为 1)，较小的输出值对应负标签(真实标签为 0  )。这在损失函数中表现为如下形式：

![format_png][]

对权重向量和偏置量，计算其对损失函数的梯度**。**

![format_png 1][]

更新权重和偏置值：

![format_png 2][]

import numpy as np
    from sklearn.model_selection import train_test_split
    import matplotlib.pyplot as plt
    from sklearn.datasets import make_blobs
    
    np.random.seed(123)
    x, y_true = make_blobs(n_samples=1000, centers=2)#n_samples待生成的样本总数,centers类别数,n_features每个样本的特征数
    # print(x.shape)#(1000,2)
    # print(y_true.shape)#一维(1000,)
    
    '数据集'
    fig = plt.figure(figsize=(8,6))
    #plt.scatter散点图；x，y是大小为(n,)的数组，即绘制散点图的数据点；c是颜色
    plt.scatter(x[:,0], x[:, 1], c=y_true)#x[:,0]是数组所有行的第一列数据，x[:,1]是数组所有行的第二列数据
    plt.title('Dataset')
    plt.xlabel('First feature')
    plt.ylabel('Second feature')
    plt.show()
    
    # Reshape targets to get column vector with shape (n_samples, 1)
    y_true = y_true[:, np.newaxis]
    # print(y_true.shape)#二维(1000,1)
    x_train, x_test, y_train, y_test = train_test_split(x, y_true)
    print('Shape of x_train: ', x_train.shape)
    print('Shape of y_train: ', y_train.shape)
    print('Shape of x_test: ', x_test.shape)
    print('Shape of y_test: ', y_test.shape)
    
    class logisticRegression:
        def __init__(self):
            pass
    
        def sigmoid(self, x):
            return 1 / (1 + np.exp(-x))
    
        def train(self, x, y_true, n_iters, l_r):
            n_samples, n_features = x.shape
            self.weight = np.zeros((n_features, 1))
            self.bias = 0
            costs = []
    
            for i in range(n_iters):
                y_predict = self.sigmoid(np.dot(x, self.weight) + self.bias)
                cost = (-1 / n_samples) * np.sum(y_true * np.log(y_predict) +
                                                 (1 - y_true) * np.log(1 - y_predict))
                dw = (1 / n_samples) * np.dot(x.T, (y_predict - y_true))
                db = (1 / n_samples) * np.sum(y_predict - y_true)
    
                self.weight = self.weight - l_r * dw
                self.bias = self.bias - l_r * db
    
                costs.append(cost)
                if(i % 100 == 0):
                    print('Cost after iteration {}:{}'.format(i, cost))
            return self.weight, self.bias, costs
    
        def predict(self, x):
            y_predict = self.sigmoid(np.dot(x, self.weight) + self.bias)
            y_predict_labels = [1 if elem > 0.5 else 0 for elem in y_predict]
            return np.array(y_predict_labels)[:, np.newaxis]
    
    regressor = logisticRegression()
    w_trained, b_trained, costs = regressor.train(x_train, y_train, n_iters=600, l_r=0.009)
    fig = plt.figure(figsize=(8,6))
    plt.plot(np.arange(600), costs)
    plt.title('Development of cost over training')
    plt.xlabel('Number of iterations')
    plt.ylabel('Cost')
    plt.show()
    
    y_p_train = regressor.predict(x_train)
    y_p_test = regressor.predict(x_test)
    print('Train accuracy: ',
          (100 - np.mean(np.abs(y_p_train - y_train))), '%')
    print('Test accuracy: ',
          (100 - np.mean(np.abs(y_p_test - y_test))), '%')

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM5OTM4NjY2_size_16_color_FFFFFF_t_70][]

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(二) 直接调用sklearn的API

from sklearn.linear_model import LogisticRegression         # 逻辑回归 #
    module = LogisticRegression()
    module.fit(x, y)
    module.score(x, y)
    module.predict(test)

完整代码：

import numpy as np
    from sklearn.model_selection import train_test_split
    import matplotlib.pyplot as plt
    from sklearn.datasets import make_blobs
    from sklearn.linear_model import LogisticRegression
    
    np.random.seed(123)
    x, y_true = make_blobs(n_samples=1000, centers=2)
    
    '数据集'
    fig = plt.figure(figsize=(8, 6))
    plt.scatter(x[:, 0], x[:, 1], c=y_true)
    plt.title('Dataset')
    plt.xlabel('First feature')
    plt.ylabel('Second feature')
    plt.show()
    
    y_true = y_true[:, np.newaxis]
    # print(y_true.shape)#二维(1000,1)
    x_train, x_test, y_train, y_test = train_test_split(x, y_true)
    print('Shape of x_train: ', x_train.shape)
    print('Shape of y_train: ', y_train.shape)
    print('Shape of x_test: ', x_test.shape)
    print('Shape of y_test: ', y_test.shape)
    
    module = LogisticRegression()
    module.fit(x_test, y_test)
    y_p_train = module.predict(x_train)
    y_p_test = module.predict(x_test)
    print('Train accuracy: ',
          (100 - np.mean(np.abs(y_p_train - y_train))), '%')
    print('Test accuracy: ',
          (100 - np.mean(np.abs(y_p_test - y_test))), '%')

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM5OTM4NjY2_size_16_color_FFFFFF_t_70 3][]

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