不使用sklearn，手动实现朴素贝叶斯分类

手动实现朴素贝叶斯分类器，你需要了解其基本原理，即利用贝叶斯定理来计算给定特征向量的概率，以及类别之间的先验概率。这里是一个简单的例子，仅用于二分类情况，使用了高斯朴素贝叶斯：

import numpy as np

class NaiveBayesClassifier:
    def __init__(self):
        self.classes_count = None
        self.class_priors = None
        self.mean_vectors = None
        self.variance_vectors = None

    def fit(self, X, y):
        self.classes_count = np.bincount(y)
        self.class_priors = self.classes_count / len(y)

        self.mean_vectors = {}
        self.variance_vectors = {}

        for class_idx, class_label in enumerate(np.unique(y)):
            class_samples = X[y == class_label]
            self.mean_vectors[class_label] = np.mean(class_samples, axis=0)
            self.variance_vectors[class_label] = np.cov(class_samples.T)

    def _gaussian_probability(self, x, mean, variance):
        # 计算单个样本x属于某类的概率，按照高斯分布
        return (1 / ((2 * np.pi) ** .5 * np.sqrt(variance))) * np.exp(-((x - mean)**2) / (2 * variance))

    def predict(self, X):
        probabilities = []
        for sample in X:
            likelihoods = []
            for class_idx, mean_vector in self.mean_vectors.items():
                likelihood = np.prod([self._gaussian_probability(x, mean, var) for x, mean, var in zip(sample, mean_vector, self.variance_vectors[class_idx])])
                likelihoods.append(likelihood * self.class_priors[class_idx])
            probabilities.append(np.argmax(likelihoods))
        return probabilities

# 使用示例
# 假设我们有一个二维的数据集（特征向量为2D数组）
data = [[0, 0], [1, 1], [0, 1], [1, 0]]
labels = [0, 0, 1, 1]

model = NaiveBayesClassifier()
model.fit(data, labels)

test_data = [[0, 0], [0.5, 0.5]]
predictions = model.predict(test_data)

在这个例子中，`fit`方法负责学习每个类别的均值和方差，`predict`方法则根据新的样本计算高斯概率并选择最有可能的类别。