先验算法的实现

import numpy as np

class NaiveBayesClassifier:
    def __init__(self):
        self.priors = {}
        self.likelihoods = {}
    
    def fit(self, X, y):
        n_samples, n_features = X.shape
        self.classes = np.unique(y)
        
        # 计算先验概率
        for c in self.classes:
            self.priors[c] = np.sum(y == c) / n_samples
        
        # 计算似然概率
        for c in self.classes:
            X_c = X[y == c]
            self.likelihoods[c] = {
                "mean": np.mean(X_c, axis=0),
                "var": np.var(X_c, axis=0)
            }
    
    def predict(self, X):
        y_pred = [self._predict(x) for x in X]
        return np.array(y_pred)
    
    def _predict(self, x):
        posteriors = []
        
        for c in self.classes:
            prior = np.log(self.priors[c])
            likelihood = np.sum(np.log(self._pdf(c, x)))
            posterior = prior + likelihood
            posteriors.append(posterior)
        
        return self.classes[np.argmax(posteriors)]
    
    def _pdf(self, class_idx, x):
        mean = self.likelihoods[class_idx]["mean"]
        var = self.likelihoods[class_idx]["var"]
        numerator = np.exp(-(x - mean) ** 2 / (2 * var))
        denominator = np.sqrt(2 * np.pi * var)
        return numerator / denominator

# 示例数据
X = np.array([[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7]])
y = np.array([0, 0, 0, 1, 1, 1])

# 训练模型
clf = NaiveBayesClassifier()
clf.fit(X, y)

# 预测
X_test = np.array([[2, 3], [5, 6]])
y_pred = clf.predict(X_test)
print("Predictions:", y_pred)