Computing Prior and Posterior Probabilities for Gaussian Mixture Models

This program computes prior and posterior probabilities for Gaussian Mixture Models (GMM). To enhance computational performance, we implement large-scale matrix operations that optimize processing speed through vectorized calculations. This approach not only accelerates probability computations but also minimizes potential numerical errors during execution. The implementation leverages matrix algebra for efficient expectation steps, where covariance matrices and mean vectors are processed in bulk operations. Additionally, we have integrated enhanced functionality for greater user control over program execution. Users can select between different algorithmic approaches (such as EM algorithm variants) for probability calculations and adjust matrix dimensions to accommodate diverse dataset sizes. The program supports dynamic memory allocation for handling large-scale GMM parameter matrices, including precision matrices and weight vectors. Key features include parallel processing of component densities using matrix multiplication for likelihood calculations, and optimized log-sum-exp operations for numerical stability during posterior probability computation. The program provides flexible configuration options for convergence thresholds and iteration limits in the probability estimation routines. In summary, this solution delivers accelerated probability computations for Gaussian Mixture Models while offering extensive customization options to adapt to various analytical requirements and data scenarios through configurable matrix operations and algorithm selection.