A Variational Approach to Bayesian Phylogenetic Inference

As a powerful statistical tool that has revolutionized modern molecular evolutionary analysis, Bayesian phylogenetic inference has been widely used for tasks ranging from genomic epidemiology [Dudas et al., 2017, du Plessis et al., 2021] to conservation genetics [DeSalle and Amato, 2004]. Given aligned sequence data (e.g., DNA, RNA or protein sequences) and a model of evolution, Bayesian phylogenetics provides principled approaches to quantify the uncertainty of the evolutionary process in terms of the posterior probabilities of phylogenetic trees [Huelsenbeck et al., 2001]. In addition to uncertainty quantification, Bayesian methods enable integrating out tree uncertainty in order to get more confident estimates of parameters of interest, such as factors in the transmission of Ebolavirus [Dudas et al., 2017]. Bayesian methods also allow complex substitution models [Lartillot and Philippe, 2004], which are important in elucidating deep phylogenetic relationships [Feuda et al., 2017]. Ever since its introduction to the phylogenetic community in the 1990s, Bayesian phylogenetic inference has been dominated by random-walk Markov chain Monte Carlo (MCMC) approaches [Yang and Rannala, 1997, Mau et al., 1999, Huelsenbeck and Ronquist, 2001, Drummond et al., 2002, 2005]. However, this approach is fundamentally limited by the complexities of tree space.