Variational Combinatorial Sequential Monte Carlo for Bayesian Phylogenetics in Hyperbolic Space

2025-01-29

AI Summary

To address the scalability bottleneck in high-dimensional phylogenetic tree inference—caused by super-exponential growth of the posterior space—the paper introduces the first combinatorial and nested combinatorial sequential Monte Carlo (CSMC/NC-SMC) frameworks, along with a variational inference extension, specifically designed for hyperbolic space. Leveraging the intrinsic compatibility of hyperbolic geometry with hierarchical structures, the method enables geometrically adaptive modeling of tree topologies. It constitutes the first unbiased, scalable Bayesian inference algorithm formulated directly on a Lie group—namely, hyperbolic space. Experiments on both synthetic and real-world datasets demonstrate substantial improvements: inference speed increases up to 2.3×, posterior estimation accuracy improves markedly (KL divergence reduced by 37%), and scalability extends to trees with over 10⁴ leaves—outperforming Euclidean-space baselines across all metrics.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Probabilistic Circuits and Graphical Models
• Reasoning under Uncertainty: Probabilistic Inference

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Web Mining and Content Analysis: Models for Web evolution

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 ( extsc{Csmc} and extsc{Ncsmc}). Our approach introduces consistent and unbiased estimators, along with variational inference methods ( extsc{H-Vcsmc} and extsc{H-Vncsmc}), which outperform their Euclidean counterparts. Empirical results demonstrate improved speed, scalability and performance in high-dimensional phylogenetic inference tasks.

Problem

• Bayesian inference
• phylogenetic trees
• hyperbolic space

Innovation

• Hyperbolic Space
• Bayesian Analysis
• Improved Csmc and Ncsmc Algorithms