python写高斯混合模型的隐变量的后验分布的代码

墨蓝 2024-03-25 12:53 37阅读 0赞

下面是一段使用python编写的高斯混合模型隐变量后验分布代码：

\`\`\` import numpy as np from scipy.stats import multivariate\_normal

class GaussianMixtureModel: def **init**(self, n\_components, max\_iter=100, tol=1e-3): self.n\_components = n\_components self.max\_iter = max\_iter self.tol = tol

def fit(self, X):
        n_samples, n_features = X.shape
        self.weights_ = np.ones(self.n_components) / self.n_components
        self.means_ = np.random.randn(self.n_components, n_features)
        self.covariances_ = np.array([np.eye(n_features)] * self.n_components)
        
        responsibilities = np.zeros((n_samples, self.n_components))
        log_likelihoods = []
        for i in range(self.max_iter):
            # E-step
            for j in range(self.n_components):
                responsibilities[:, j] = self.weights_[j] * \
                    multivariate_normal.pdf(X, mean=self.means_[j], cov=self.covariances_[j])
            responsibilities /= responsibilities.sum(axis=1, keepdims=True)
            
            # M-step
            n_responsibilities = responsibilities.sum(axis=0)
            self.weights_ = n_responsibilities / n_samples
            self.means_ = (responsibilities.T @ X) / n_responsibilities[:, None]
            self.covariances_ = np.zeros((self.n_components, n_features, n_features))
            for j in range(self.n_components):
                delta = X - self.means_[j]
                self.covariances_[j] = (responsibilities[:, j, None, None] * delta).T @ delta / n_responsibilities[j]
            
            # Calculate log likelihood
            log_likelihood = 0
            for j in range(self.n_components):
                log_likelihood += self.weights_[j] * \
                    multivariate_normal.pdf(X, mean=self.means_[j], cov=self.covariances_[j])
            log_likelihood = np.log(log_likelihood).sum()
            log_likelihoods.append(log_likelihood)
            
            # Check convergence
            if i > 0 and np.abs(log_likelihoods[-1] - log_likelihoods[-2]) < self.tol:
                break
                
        return log_likelihoods
    
    def predict(self, X):
        n_samples, n_features = X.shape
        responsibilities = np.zeros((n_samples, self.n_components))
        for