Gaussian Mixture Clustering

Implement:

def gmm_e_step(input, weights, means, variances) -> np.ndarray:
    """Returns shape (n_samples, k) responsibilities."""

def gmm_m_step(input, responsibilities) -> tuple[np.ndarray, np.ndarray, np.ndarray]:
    """Returns updated (weights, means, variances)."""

• Reuse 03-gaussian-naive-bayes's gaussian_log_likelihood.
• Diagonal covariance only, variances[j] is one number per feature, per component, no cross-feature covariance terms.