Variational Combinatorial Sequential Monte Carlo for Bayesian Phylogenetics in Hyperbolic Space
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909690219200512 |
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| author | Chen, Alex Chlenski, Philipe Munyuza, Kenneth Moretti, Antonio Khalil Naesseth, Christian A. Pe'er, Itsik |
| author_facet | Chen, Alex Chlenski, Philipe Munyuza, Kenneth Moretti, Antonio Khalil Naesseth, Christian A. Pe'er, Itsik |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_17965 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Variational Combinatorial Sequential Monte Carlo for Bayesian Phylogenetics in Hyperbolic Space Chen, Alex Chlenski, Philipe Munyuza, Kenneth Moretti, Antonio Khalil Naesseth, Christian A. Pe'er, Itsik Machine Learning 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. |
| title | Variational Combinatorial Sequential Monte Carlo for Bayesian Phylogenetics in Hyperbolic Space |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2501.17965 |