A1426
Title: Bayesian graphical models under positivity constraints: A scalable generalized likelihood approach
Authors: Kshitij Khare - University of Florida (United States) [presenting]
Abstract: A computationally scalable Bayesian framework for precision matrix estimation in Gaussian graphical models under total positivity constraints is developed. To overcome the high computational cost of the Gaussian likelihood, a generalized Bayesian approach based on the D-trace loss is adopted, which eliminates the log-determinant term and enables efficient optimization while allowing relaxation of positive definiteness during sampling. Sparsity is induced via spike-and-slab priors, and the resulting generalized posterior is shown to be proper under mild conditions. A suite of efficient posterior sampling algorithms tailored to high-dimensional settings is introduced, starting from a component-wise Gibbs sampler with a novel data augmentation scheme that induces conditional independence among precision matrix entries, enabling joint updates. By exploiting the Gram structure of the sample covariance matrix, a fast matrix-normal sampler is developed that significantly reduces per-iteration complexity in high-dimensional settings. An interweaving strategy combines augmented and direct updates to improve mixing without sacrificing scalability. Experiments on synthetic and financial data demonstrate substantial computational gains over existing methods, while maintaining competitive estimation accuracy and improved recovery of structured dependencies.
