逻辑回归
学习逻辑回归原理
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实现代码
import numpy as np import matplotlib.pyplot as plt from sklearn import datasets from sklearn.model_selection import train_test_split # 因为逻辑回归是分类问题，因此需要对评价指标进行更改 #from .metrics import accuracy_score class LogisticRegression: def __init__(self): """初始化Logistic Regression模型""" self.coef_ = None self.intercept_ = None self._theta = None """ 定义sigmoid方法 参数：线性模型t 输出：sigmoid表达式 """ def _sigmoid(self, t): return 1. / (1. + np.exp(-t)) """ fit方法，内部使用梯度下降法训练Logistic Regression模型 参数：训练数据集X_train, y_train, 学习率, 迭代次数 输出：训练好的模型 """ def fit(self, X_train, y_train, eta=0.01, n_iters=1e4): assert X_train.shape[0] == y_train.shape[0], \ "the size of X_train must be equal to the size of y_train" """ 定义逻辑回归的损失函数 参数：参数theta、构造好的矩阵X_b、标签y 输出：损失函数表达式 """ def J(theta, X_b, y): # 定义逻辑回归的模型：y_hat y_hat = self._sigmoid(X_b.dot(theta)) try: # 返回损失函数的表达式 return - np.sum(y * np.log(y_hat) + (1 - y) * np.log(1 - y_hat)) / len(y) except: return float('inf') """ 损失函数的导数计算 参数：参数theta、构造好的矩阵X_b、标签y 输出：计算的表达式 """ def dJ(theta, X_b, y): return X_b.T.dot(self._sigmoid(X_b.dot(theta)) - y) / len(y) """ 梯度下降的过程 """ def gradient_descent(X_b, y, initial_theta, eta, n_iters=1e4, epsilon=1e-8): theta = initial_theta cur_iter = 0 while cur_iter < n_iters: gradient = dJ(theta, X_b, y) last_theta = theta theta = theta - eta * gradient if (abs(J(theta, X_b, y) - J(last_theta, X_b, y)) < epsilon): break cur_iter += 1 return theta X_b = np.hstack([np.ones((len(X_train), 1)), X_train]) initial_theta = np.zeros(X_b.shape[1]) # 梯度下降的结果求出参数heta self._theta = gradient_descent(X_b, y_train, initial_theta, eta, n_iters) # 第一个参数为截距 self.intercept_ = self._theta[0] # 其他参数为各特征的系数 self.coef_ = self._theta[1:] return self """ 逻辑回归是根据概率进行分类的，因此先预测概率 参数：输入空间X_predict 输出：结果概率向量 """ def predict_proba(self, X_predict): """给定待预测数据集X_predict，返回表示X_predict的结果概率向量""" assert self.intercept_ is not None and self.coef_ is not None, \ "must fit before predict!" assert X_predict.shape[1] == len(self.coef_), \ "the feature number of X_predict must be equal to X_train" X_b = np.hstack([np.ones((len(X_predict), 1)), X_predict]) # 将梯度下降得到的参数theta带入逻辑回归的表达式中 return self._sigmoid(X_b.dot(self._theta)) """ 使用X_predict的结果概率向量，将其转换为分类 参数：输入空间X_predict 输出：分类结果 """ def predict(self, X_predict): """给定待预测数据集X_predict，返回表示X_predict的结果向量""" assert self.intercept_ is not None and self.coef_ is not None, \ "must fit before predict!" assert X_predict.shape[1] == len(self.coef_), \ "the feature number of X_predict must be equal to X_train" # 得到概率 proba = self.predict_proba(X_predict) # 判断概率是否大于0.5，然后将布尔表达式得到的向量，强转为int类型，即为0-1向量 return np.array(proba >= 0.5, dtype='int') def score(self, X_test, y_test): """根据测试数据集 X_test 和 y_test 确定当前模型的准确度""" y_predict = self.predict(X_test) return accuracy_score(y_test, y_predict) def __repr__(self): return "LogisticRegression()" iris = datasets.load_iris() X = iris.data y = iris.target X = X[y<2,:2] y = y[y<2] plt.scatter(X[y==0,0], X[y==0,1], color="red") plt.scatter(X[y==1,0], X[y==1,1], color="blue") plt.show() X_train, X_test, y_train, y_test = train_test_split(X, y, seed=666) log_reg = LogisticRegression() log_reg.fit(X_train, y_train) # 查看训练数据集分类准确度 log_reg.score(X_test, y_test) """ 输出：1.0 """ # 查看逻辑回归得到的概率 log_reg.predict_proba(X_test) """ 输出： array([ 0.92972035, 0.98664939, 0.14852024, 0.17601199, 0.0369836 , 0.0186637 , 0.04936918, 0.99669244, 0.97993941, 0.74524655, 0.04473194, 0.00339285, 0.26131273, 0.0369836 , 0.84192923, 0.79892262, 0.82890209, 0.32358166, 0.06535323, 0.20735334]) """ # 得到逻辑回归分类结果 log_reg.predict(X_test) """ 输出： array([1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0]) """