Improved Variational Bayesian Phylogenetic Inference Using Mixtures

Abstract

We introduce VBPI-Mixtures, an algorithm aimed at improving the precision of phylogenetic posterior distributions, with a focus on accurately approximating tree-topologies and branch lengths. Although Variational Bayesian Phylogenetic Inference (VBPI)—a state-of-the-art black-box variational inference (BBVI) framework—has achieved significant success in approximating these distributions, it faces challenges in dealing with the multimodal nature of tree-topology posteriors. While advanced deep learning techniques like normalizing flows and graph neural networks have enhanced VBPI's approximations of branch-length posteriors, there has been a gap in improving its tree-topology posterior approximations. Our novel VBPI-Mixtures algorithm addresses this gap by leveraging recent advancements in mixture learning within the BBVI domain. Consequently, VBPI-Mixtures can capture distributions over tree-topologies that other VBPI algorithms cannot model. Across eight real phylogenetic datasets and compared to the considered benchmarks, we show that VBPI-Mixtures result in lower-variance estimators of the marginal log-likelihood and smaller KL divergences to an MCMC-based approximation of the true tree-topology posterior.