Implementation of Cross-Entropy for Optimizing Multivariate Gaussian Mixture Models

This article provides source code implementing cross-entropy optimization for multivariate Gaussian mixture models, designed for educational and practical use. The code employs cross-entropy techniques to optimize multivariate Gaussian mixture models, enhancing both model accuracy and computational performance. Key implementation aspects include probability distribution handling through NumPy arrays, entropy calculations using logarithmic functions, and iterative optimization via the Expectation-Maximization (EM) algorithm. The EM algorithm implementation features E-step responsibilities calculation using Gaussian probability density functions and M-step parameter updates through weighted maximum likelihood estimation. The code demonstrates advanced machine learning concepts including mixture model initialization with K-means clustering, covariance regularization for numerical stability, and convergence monitoring using likelihood change thresholds. By studying this implementation, developers can deepen their understanding of multivariate Gaussian distributions, mixture model architectures, and cross-entropy optimization mechanics. The modular code structure serves as a practical reference for custom GMM implementations, featuring configurable components for covariance types (full, diagonal, tied) and model selection criteria (AIC/BIC). Users can adapt this foundation for projects involving density estimation, clustering applications, or anomaly detection systems.