Gene Coexpression Analysis with Dirichlet Mixture Model: Accelerating Model Evaluation Through Closed-Form KL Divergence Approximation Using Variational Techniques

Gene coexpression analysis poses unique challenges, particularly in clustering normalized gene profiles where dedicated algorithms are lacking. Compositional in nature, normalized gene profiles find a fitting solution in the Dirichlet Mixture Model (DMM). This study pioneers the application of DMM for clustering normalized gene profiles, recognizing the necessity for efficient model evaluation. Central to this evaluation is the Kullback-Leibler (KL) Divergence, a critical metric for DMMs. In addressing the computational challenges associated with KL Divergence in DMMs, we introduce a novel variational approach. This method provides a closed-form solution, markedly improving computational efficiency for rapid model comparisons and robust estimation evaluations. Through validation on real and simulated data, our approach demonstrates superior efficiency and accuracy compared to traditional Monte Carlo-based methods. This innovation opens new frontiers for expeditious exploration of diverse DMM models, propelling advancements in the statistical analysis of compositional gene expression data.