2025/01/29 by Alex Chen, Philipe Chlenski, Chen, Alex +9 · 3 citations
Computer Science · Mathematics · #Algorithms and Data Compression #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Markov Chains and Monte Carlo Methods
paper · pdf · doi:10.48550/arxiv.2501.17965
openalex publication_date 2025/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 (Csmc and Ncsmc). Our approach introduces consistent and unbiased estimators, along with variational inference methods (H-Vcsmc and H-Vncsmc), which outperform their Euclidean counterparts. Empirical results demonstrate improved speed, scalability and performance in high-dimensional phylogenetic inference tasks.