Adaptive Importance Sampling Based Surrogation Methods for Bayesian Hierarchical Models, via Logarithmic Integral Optimization

We explore Maximum a Posteriori inference of Bayesian Hierarchical Models (BHMs) with intractable normalizers, which are increasingly prevalent in contemporary applications and pose computational challenges when combined with nonconvexity and nondifferentiability. To address these, we propose the Adaptive Importance Sampling-based Surrogation method, which efficiently handles nonconvexity and nondifferentiability while improving the sampling approximation of the … Read more

Comparing Solution Paths of Sparse Quadratic Minimization with a Stieltjes Matrix

This paper studies several solution paths of sparse quadratic minimization problems as a function of the weighing parameter of the bi-objective of estimation loss versus solution sparsity. Three such paths are considered: the “L0-path” where the discontinuous L0-function provides the exact sparsity count; the “L1-path” where the L1-function provides a convex surrogate of sparsity count; … Read more