Universal probabilistic programming offers a powerful approach to statistical phylogenetics

Abstract

Statistical phylogenetic analysis currently relies on complex, dedicated software packages, making it difficult for evolutionary biologists to explore new models and inference strategies. Recent years have seen more generic solutions based on probabilistic graphical models, but this formalism can only partly express phylogenetic problems. Here, we show that universal probabilistic programming languages (PPLs) solve the expressivity problem, while still supporting automated generation of efficient inference algorithms. To prove the latter point, we develop automated generation of sequential Monte Carlo (SMC) algorithms for PPL descriptions of arbitrary biological diversification (birth-death) models. SMC is a new inference strategy for these problems, supporting both parameter inference and efficient estimation of Bayes factors that are used in model testing. We take advantage of this in automatically generating SMC algorithms for several recent diversification models that have been difficult or impossible to tackle previously. Finally, applying these algorithms to 40 bird phylogenies, we show that models with slowing diversification, constant turnover and many small shifts generally explain the data best. Our work opens up several related problem domains to PPL approaches, and shows that few hurdles remain before these techniques can be effectively applied to the full range of phylogenetic models.

Correctness of Sequential Monte Carlo Inference for Probabilistic Programming Languages

“…This strategy is far from optimal, however. For instance, only resampling at #3, which is encountered the same number of times in each execution, performs much better [21,30]. Our results show that this is correct as well, and that it gives the same asymptotic results as the naive strategy in the previous paragraph.…”

“…The example is written in a functional PPL 3 developed as part of this paper, in order to verify Fig. 1: A simplified version of a phylogenetic birth-death model from [30]. See the text for a description.…”

“…Consider the program in Fig. 1, encoding a simplified version of a phylogenetic birth-death model (see Ronquist et al [30] for the full version). The problem is to find the model evidence for a particular birth rate (lambda = 0.2) and death rate (mu = 0.1), given an observed phylogenetic tree.…”

“…Probabilistic programming is a programming paradigm for probabilistic models, encompassing a wide range of programming languages, libraries, and platforms [5,13,14,25,32,37,38]. Such probabilistic models are typically created to express inference problems, which are ubiquitous and highly significant in, for instance, machine learning [1], artificial intelligence [31], phylogenetics [29,30], and topic modeling [2].…”

“…As a consequence of (ii), SMC also correctly approximates t , and in turn the target measure t . Crucially, this also means estimating the model evidence (likelihood), which allows for compositionality [15] and comparisons between different models [30]. This contribution is summarized in Theorem 3.…”