# Variational Combinatorial Sequential Monte Carlo for Bayesian Phylogenetics in Hyperbolic Space

arXiv: https://arxiv.org/abs/2501.17965 · HTML: https://mlsanity.com/paper/2501.17965/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 35 references that are in the map.
- First posted on arXiv 29 Jan 2025.

## Builds on (most cited first, 11 of 11)

- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Nested Sequential Monte Carlo Methods](https://mlsanity.com/paper/1502.02536/) (2015)
- [Improved Variational Bayesian Phylogenetic Inference with Normalizing Flows](https://mlsanity.com/paper/2012.00459/) (2020)
- [Neural Distance Embeddings for Biological Sequences](https://mlsanity.com/paper/2109.09740/) (2021)
- [Learnable Topological Features for Phylogenetic Inference via Graph Neural Networks](https://mlsanity.com/paper/2302.08840/) (2023)
- [Variational Combinatorial Sequential Monte Carlo Methods for Bayesian Phylogenetic Inference](https://mlsanity.com/paper/2106.00075/) (2021)
- [GeoPhy: Differentiable Phylogenetic Inference via Geometric Gradients of Tree Topologies](https://mlsanity.com/paper/2307.03675/) (2023)
- [VaiPhy: a Variational Inference Based Algorithm for Phylogeny](https://mlsanity.com/paper/2203.01121/) (2022)
- [High-dimensional Filtering using Nested Sequential Monte Carlo](https://mlsanity.com/paper/1612.09162/) (2016)
- [Variational Pseudo Marginal Methods for Jet Reconstruction in Particle Physics](https://mlsanity.com/paper/2406.03242/) (2024)

## Built on by (most cited first, 3 of 3)

- [Hyperbolic Genome Embeddings](https://mlsanity.com/paper/2507.21648/) (2025)
- [Randomized HyperSteiner: A Stochastic Delaunay Triangulation Heuristic for the Hyperbolic Steiner Minimal Tree](https://mlsanity.com/paper/2510.09328/) (2025)
- [Deep Generative Models for Phylogenetic Inference with Complex Evolutionary Processes](https://mlsanity.com/paper/2610.19053/) (2026)

## Abstract (arXiv)

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