ICML 2025

Variational Phylogenetic Inference with Products over Bipartitions
Evan Sidrow 1 Alexandre Bouchard-Cˆot´e 2 Lloyd T. Elliott 1
Abstract
Bayesian phylogenetics is vital for understanding
evolutionary dynamics, and requires accurate and
efficient approximation of posterior distributions
over trees. In this work, we develop a variational
Bayesian approach for ultrametric phylogenetic
trees. We present a novel variational family based
on coalescent times of a single-linkage clustering
and derive a closed-form density for the resulting
distribution over trees. Unlike existing methods
for ultrametric trees, our method performs infer-
ence over all of tree space, it does not require
any Markov chain Monte Carlo subroutines, and
our variational family is differentiable. Through
experiments on benchmark genomic datasets and
an application to the viral RNA of SARS-CoV-2,
we demonstrate that our method achieves compet-
itive accuracy while requiring significantly fewer
gradient evaluations than existing state-of-the-art
techniques.
1. Introduction
The goal of Bayesian phylogenetics is to infer the genealogy
of a collection of taxa given a genetic model and aligned
sequence data. Phylogenetics is used in fields such as epi-
demiology (Li et al., 2020), linguistics (List et al., 2014), and
ecology (Godoy et al., 2018). Bayesian phylogenetic infer-
ence quantifies uncertainty and integrates over phylogenetic
tree structures within a phylogenetic model (Zhang and Mat-
sen IV, 2019). Most Bayesian phylogenetic inference is per-
formed using Markov chain Monte Carlo (MCMC) methods
with candidate trees iteratively proposed and either accepted
or rejected based on their consistency with the observed data.
However, MCMC methods can struggle because the number
of possible trees grows super-exponentially in the number
of taxa and posteriors on trees are highly multi-modal.
1Department of Statistics and Actuarial Science, Simon Fraser
University, Burnaby, Canada 2Department of Statistics...