Variational Combinatorial Sequential Monte Carlo for Bayesian Phylogenetics in Hyperbolic Space

TL;DR

This paper introduces hyperbolic space-based variational combinatorial sequential Monte Carlo methods for efficient and scalable Bayesian phylogenetic inference, leveraging hyperbolic geometry to better model hierarchical structures.

Contribution

It develops novel hyperbolic extensions of combinatorial sequential Monte Carlo algorithms with unbiased estimators and variational inference, improving inference speed and scalability.

Findings

Outperforms Euclidean methods in speed and scalability

Provides unbiased estimators for hyperbolic inference

Enhances high-dimensional phylogenetic analysis

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 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 phylogenetic inference tasks.