Papers › Variational Combinatorial Sequential Monte Carlo for Bayesian Phylogenetics in Hyperbolic Space

Variational Combinatorial Sequential Monte Carlo for Bayesian Phylogenetics in Hyperbolic Space

29 Jan 2025arXiv:2501.17965archive 2025-07-28

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

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.

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