Improved Variational Bayesian Phylogenetic Inference using Mixtures

We present VBPI-Mixtures, an algorithm designed to enhance the accuracy of phylogenetic posterior distributions, particularly for tree-topology and branchlength approximations. Despite the Variational Bayesian Phylogenetic Inference (VBPI), a leading-edge black-box variational inference (BBVI) framework, achieving remarkable approximations of these distributions, the multimodality of the tree-topology posterior presents a formidable challenge to sampling-based learning techniques such as BBVI. Advanced deep learning methodologies such as normalizing flows and graph neural networks have been explored to refine the branch-length posterior approximation, yet efforts to ameliorate the posterior approximation over tree topologies have been lacking. As a result, VBPI-Mixtures is capable of capturing distributions over tree-topologies that VBPI fails to model. We deliver state-ofthe-art performance on difficult density estimation tasks across numerous real phylogenetic datasets. Phylogenetic inference has a wide range of applications in various fields, such as molecular evolution, epidemiology, ecology, and tumor progression, making it an essential tool for modern evolutionary research. Bayesian phylogenetics allows researchers to reason about uncertainty in their findings about the evolutionary relationship between species. The posterior distribution over phylogenetic trees given the species data is, however, challenging to infer, since the latent space is a Cartesian product of the discrete tree-topology space and the continuous branch-length space. Furthermore, the cardinality of the tree-topology space grows as a double factorial of the number of species (taxa), making the marginal likelihood computationally intractable in most interesting problem settings.