VaiPhy: a Variational Inference Based Algorithm for Phylogeny
Authors: Hazal Koptagel, Oskar Kviman, Harald Melin, Negar Safinianaini, Jens Lagergren

Phylogenetics is a classical methodology in computational biology that today has become highly relevant for medical investigation of single-cell data, e.g., in the context of development of cancer.  The exponential size of the tree space is unfortunately a formidable obstacle for current Bayesian phylogenetic inference using Markov chain Monte Carlo based methods since these rely on local operations. And although more recent variational inference (VI) based methods offer speed improvements, they rely on expensive auto-differentiation operations for learning the variational parameters. We propose VaiPhy, a remarkably fast VI based algorithm for approximate posterior inference in an \textit{augmented tree space}. VaiPhy produces marginal log-likelihood estimates on par with the state-of-the-art methods on real data, and is considerably faster since it does not require auto-differentiation. Instead, VaiPhy combines coordinate ascent update equations with two novel sampling schemes: (i) \textit{SLANTIS}, a proposal distribution for tree topologies in the augmented tree space, and (ii) the \textit{JC sampler}, the, to the best of our knowledge, first ever scheme for sampling branch lengths directly from the popular Jukes-Cantor model. We compare VaiPhy in terms of density estimation and runtime. Additionally, we evaluate the reproducibility of the baselines. We provide our code on GitHub: \url{https://github.com/Lagergren-Lab/VaiPhy}.