Variational Combinatorial Sequential Monte Carlo for Bayesian Phylogenetics in Hyperbolic Space

Alex Chen, Philippe Chlenski, Kenneth Munyuza, Antonio Khalil Moretti, Christian A. Naesseth, Itsik Pe'er

TL;DR: The paper presents H-VCSMC, a hyperbolic extension of Combinatorial SMC methods that enhances performance for hierarchical structures compared to traditional Euclidean approaches.

Abstract: Hyperbolic space naturally encodes hierarchical structures such as phylogenies (binary trees), where inward-bending geodesics reflect paths through least common ancestors, and the exponential growth of neighborhoods mirrors the super-exponential scaling of topologies. This scaling challenge limits the efficiency of Euclidean-based approximate Bayesian inference methods. Motivated by the geometric connections between trees and hyperbolic space, we develop novel hyperbolic extensions of two sequential search algorithms: Combinatorial and Nested Combinatorial Sequential Monte Carlo (\textsc{Csmc} and \textsc{Ncsmc}). Our approach introduces consistent and unbiased estimators, along with variational inference methods (\textsc{H-Vcsmc} and \textsc{H-Vncsmc}), which outperform their Euclidean counterparts. Empirical results demonstrate improved speed, scalability and performance in high-dimensional Bayesian phylogenetic inference tasks.

Submission Number: 1028