Title: From Stationary Points to Global Structure: Constrained Maximum Likelihood Estimation and Haplotype Phasing

Speaker: Derek Aguiar, Associate Professor, School of Computing, University of Connecticut

Time: 3:30 PM - 4:30 PM, Austin 105

Abstract: Maximum likelihood estimation can lead to highly nonconvex optimization problems with exponentially large latent spaces, making global optimization appear computationally infeasible. We describe a class of likelihood problems with constant-sum parameter constraints for which the stationary points have an unexpectedly useful structure. By examining the constrained first-order conditions, we obtain a fixed-point mapping that characterizes nontrivial stationary points and connects naturally to expectation-maximization. For the homogeneous likelihoods considered here, this mapping admits a convex-combination interpretation that reveals constraints shared by all stationary points. We further show that, under appropriate conditions, variables can be eliminated while preserving a global optimum. We then consider maximum likelihood haplotype phasing, an NP-hard problem in statistical genetics. For this problem, a graph representation of the likelihood provides an additional combinatorial route to variable elimination: graph homomorphisms identify groups of haplotypes that can be collapsed while preserving a maximum likelihood solution. This leads to CorePhase, an algorithm that reduces the problem to an irreducible core and makes maximum likelihood haplotype phasing practical across simulated and experimental datasets.

Bio of Derek Aguiar: Derek Aguiar is an Associate Professor in UConn’s School of Computing, where he runs the Efficient Learning and Graph Algorithm Techniques for Omics (EL GATO) Lab. The group develops Bayesian machine learning models, combinatorial algorithms, and scalable inference methods, primarily for high-dimensional biological data. Recent work spans complex disease, transcriptomics, genome structure, and haplotype inference, including non-B DNA prediction, transcript reconstruction and quantification, disease risk modeling, and haplotype assembly, phasing, and clustering. He also tends to a menagerie of domestic cats, wild birds, and other animals in his humble Connecticut abode.