Mixture-of-experts Wishart model for covariance matrices with an application to Cancer drug screening

Abstract: Covariance matrices arise naturally in different scientific fields, including finance, genomics, and neuroscience, where they encode dependence structures and reveal essential features of complex multivariate systems. In this work, we introduce a comprehensive Bayesian framework for analyzing heterogeneous covariance data through both classical mixture models and a novel mixture-of-experts Wishart (MoE-Wishart) model. The proposed MoE-Wishart model extends standard Wishart mixtures by allowing mixture weights to depend on predictors through a multinomial logistic gating network. This formulation enables the model to capture complex, nonlinear heterogeneity in covariance structures and to adapt subpopulation membership probabilities to covariate-dependent patterns. To perform inference, we develop an efficient Gibbs-within-Metropolis-Hastings sampling algorithm tailored to the geometry of the Wishart likelihood and the gating network. We additionally derive an Expectation-Maximization algorithm for maximum likelihood estimation in the mixture-of-experts setting. Extensive simulation studies demonstrate that the proposed Bayesian and maximum likelihood estimators achieve accurate subpopulation recovery and estimation under a range of heterogeneous covariance scenarios. Finally, we present an innovative application of our methodology to a challenging dataset: cancer drug sensitivity profiles, illustrating the ability of the MoE-Wishart model to leverage covariance across drug dosages and replicate measurements. Our methods are implemented in the \texttt{R} package \texttt{moewishart} available at https://github.com/zhizuio/moewishart .