混合高斯贝叶斯模型代码

混合高斯贝叶斯模型的代码如下所示：

import numpy as np
from scipy.stats import multivariate_normal

class GaussianMixtureBayes:
    def __init__(self, k, max_iter=100, eps=1e-6):
        self.k = k
        self.max_iter = max_iter
        self.eps = eps

    def fit(self, X):
        n, d = X.shape

        # 初始化每个高斯分布的均值、协方差矩阵和权重
        means = np.random.randn(self.k, d)
        covs = np.array([np.eye(d)] * self.k)
        weights = np.ones(self.k) / self.k

        for _ in range(self.max_iter):
            # E 步，计算每个样本属于每个高斯分布的概率
            probs = np.zeros((n, self.k))
            for i in range(self.k):
                probs[:, i] = weights[i] * multivariate_normal.pdf(X, means[i], covs[i])
            probs /= probs.sum(axis=1, keepdims=True)

            # M 步，更新每个高斯分布的均值、协方差矩阵和权重
            for i in range(self.k):
                weight_sum = probs[:, i].sum()
                means[i] = (probs[:, i] @ X) / weight_sum
                covs[i] = ((probs[:, i] * (X - means[i]).T) @ (X - means[i])) / weight_sum
                weights[i] = weight_sum / n

            # 计算对数似然函数值
            log_likelihood = np.log(probs @ weights).sum()
            if np.abs(log_likelihood - self.log_likelihood) < self.eps:
                break
            self.log_likelihood = log_likelihood

        self.means = means
        self.covs = covs
        self.weights = weights

    def predict(self, X):
        probs = np.zeros((X.shape[0], self.k))
        for i in range(self.k):
            probs[:, i] = self.weights[i] * multivariate_normal.pdf(X, self.means[i], self.covs[i])
        return np.argmax(probs, axis=1)

在这里，我们使用 `scipy.stats` 中的 `multivariate_normal` 函数来计算多元高斯分布的概率密度函数。`fit` 方法用来训练模型，`predict` 方法用来预测新样本的类别。注意，这个代码仅适用于连续型变量。如果数据集同时包含离散和连续型变量，需要对每个分量采用适当的概率分布进行建模。