VaiPhy: a Variational Inference Based Algorithm for Phylogeny

Abstract

Phylogenetics is a classical methodology in com- putational biology that today has become highly relevant for medical investigation of single-cell data, e.g., in the context of development of can- cer. 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 re- cent variational inference (VI) based methods of- fer speed improvements, they rely on expensive auto-differentiation operations for learning the variational parameters. We propose VaiPhy, a remarkably fast VI based algorithm for approx- imate posterior inference in an augmented tree space. VaiPhy produces marginal log-likelihood estimates on par with the state-of-the-art meth- ods on real data, and is considerably faster since it does not require auto-differentiation. Instead, VaiPhy combines coordinate ascent update equa- tions with two novel sampling schemes: (i) SLANTIS, a proposal distribution for tree topolo- gies in the augmented tree space, and (ii) the 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 esti- mation and runtime. Additionally, we evaluate the reproducibility of the baselines. We provide our code on GitHub: https://github.com/ Lagergren-Lab/VaiPhy. QC 20220421</p