Variational Supertrees for Bayesian Phylogenetics

• Published in: Bulletin of mathematical biology Vol. 86; no. 9; p. 114
• Main Authors: Karcher, Michael D., Zhang, Cheng, Matsen, Frederic A.
• Format: Journal Article
• Language: English
• Published: New York Springer US 2024; Springer Nature B.V
• Subjects: Algorithms; Bayes Theorem; Bayesian analysis; Cell Biology; Computer Simulation; Datasets; Geographical distribution; Life Sciences; Markov Chains; Mathematical and Computational Biology; Mathematical Concepts; Mathematics; Mathematics and Statistics; Models, Genetic; Original; Original Article; Phylogenetics; Phylogeny; Probability; Topology; Gradient descent; 92D30; 92D20; Variational methods; Supertrees; 92-08; Phylogenetics; 62-08; Divide-and-conquer; 49-04; 49N99
• ISSN: 0092-8240; 1522-9602; 1522-9602
• DOI: 10.1007/s11538-024-01338-5

Bayesian phylogenetic inference is powerful but computationally intensive. Researchers may find themselves with two phylogenetic posteriors on overlapping data sets and may wish to approximate a combined result without having to re-run potentially expensive Markov chains on the combined data set. This raises the question: given overlapping subsets of a set of taxa (e.g. species or virus samples), and given posterior distributions on phylogenetic tree topologies for each of these taxon sets, how can we optimize a probability distribution on phylogenetic tree topologies for the entire taxon set? In this paper we develop a variational approach to this problem and demonstrate its effectiveness. Specifically, we develop an algorithm to find a suitable support of the variational tree topology distribution on the entire taxon set, as well as a gradient-descent algorithm to minimize the divergence from the restrictions of the variational distribution to each of the given per-subset probability distributions, in an effort to approximate the posterior distribution on the entire taxon set.