Sparse Estimation in Finite Mixtures of Varying Coefficient and Survival Regression Models

Finite mixture models are foundational tools in statistical modeling, offering flexible representations for heterogeneous populations. A key subclass is the finite mixture of regression models, where each mixture component is characterized by its own regression structure influenced by covariates. In high-dimensional settings—common in areas such as genomics—use of these models presents significant challenges, particularly in variable selection and parameter estimation, necessitating the development of sparse estimation techniques. This talk explores two extensions of finite mixture regression models under high dimensionality. The first generalizes the standard finite mixture framework by incorporating varying coefficient models, where covariate effects are allowed to change with respect to an index variable (e.g., time). This approach captures dynamic relationships and latent subpopulation heterogeneity. The second extension involves finite mixtures of accelerated failure time (AFT) models, designed for survival data subject to right censoring and latent class structures. We discuss penalized estimation techniques for simultaneous variable selection and parameter estimation in both modeling frameworks. Applications to genomic datasets will be presented to illustrate the practical performance and interpretability of the proposed methods, highlighting their utility in uncovering biologically relevant patterns in complex, high-dimensional data.