Variational Combinatorial Sequential Monte Carlo for Bayesian Phylogenetics in Hyperbolic Space
This work addresses scaling issues in Bayesian phylogenetics for researchers in computational biology, offering incremental improvements over existing methods.
The paper tackled the challenge of scaling phylogenetic inference by leveraging hyperbolic space's natural encoding of hierarchical structures, developing novel hyperbolic extensions of sequential Monte Carlo methods that outperformed Euclidean counterparts with improved speed, scalability, and performance in high-dimensional tasks.
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.