A1746
Title: Mixture of multivariate linear models with heteroscedastic covariance matrices
Authors: Keunbaik Lee - Sungkyunkwan University (Korea, South) [presenting]
Abstract: A critical research gap in mixture of experts models for multivariate heteroscedastic data is addressed, specifically where covariance matrices vary as a function of covariates. A systematic framework is established through a mixture model architecture integrated with the Expectation-Maximization (EM) algorithm. Hypersphere decomposition is introduced for the structured modeling of covariance matrices, strategically employed to circumvent the inherent challenges of maintaining positive definiteness in high-dimensional covariance structures, a frequent technical impediment in complex statistical modeling. The approach successfully characterizes data exhibiting heteroscedasticity across multiple latent clusters. Through extensive numerical simulations and empirical data analysis, the theoretical soundness and practical efficacy of the proposed methodology are validated, confirming its robustness. The primary contribution lies in the implementation of multivariate mixture regression models in analytical environments that were previously avoided due to their computational complexity. This methodology provides a sophisticated and pragmatic analytical tool for scenarios characterized by covariate-dependent variance and intricate correlation structures.
