~/jan.kudlicka

Probabilistic Programming for Birth-Death Models of Evolution

J. Kudlicka

Acta Universitatis Upsaliensis, Uppsala, 2021

Abstract

Phylogenetic birth-death models constitute a family of generative models of evolution. In these models an evolutionary process starts with a single species at a certain time in the past, and the speciations—splitting one species into two descendant species—and extinctions are modeled as events of non-homogenous Poisson processes. Different birth-death models admit different types of changes to the speciation and extinction rates.

The result of an evolutionary process is a binary tree called a phylogenetic tree, or phylogeny, with the root representing the single species at the origin, internal nodes speciation events, and leaves currently living—extant—species (in the present time) and extinction events (in the past). Usually only a part of this tree, corresponding to the evolution of the extant species and their ancestors, is known via reconstruction from e.g. genomic sequences of these extant species.

The task of our interest is to estimate the parameters of birth-death models given this reconstructed tree as the observation. While encoding the generative birth-death models as computer programs is easy and straightforward, developing and implementing bespoke inference algorithms are not. This complicates prototyping, development, and deployment of new birth-death models.

Probabilistic programming is a new approach in which the generative models are encoded as computer programs in languages that include support for random variables, conditioning on the observed data, as well as automatic inference. This thesis is based on a collection of papers in which we demonstrate how to use probabilistic programming to solve the above-mentioned task of parameter inference in birth-death models. We show how these models can be implemented as simple programs in probabilistic programming languages. Our contribution also includes general improvements of the automatic inference methods.

Keywords

Probabilistic programming, birth-death models, statistical phylogenetics, particle filters, sequential Monte Carlo (SMC).

Files

Included papers

  1. F. Ronquist†, J. Kudlicka†, V. Senderov†, J. Borgström, N. Lartillot, D. Lundén, L. Murray, T. B. Schön, and D. Broman. Universal probabilistic programming offers a powerful approach to statistical phylogenetics. Preprint at https://www.biorxiv.org/content/10.1101/2020.06.16.154443v4, 2020.

    † Equal contribution.

    PDF from biorxiv.org, PDF with supplementary information from biorxiv.org

  2. J. Kudlicka, L. M. Murray, F. Ronquist, and T. B. Schön. Probabilistic programming for birth-death models of evolution using an alive particle filter with delayed sampling. In Conference on Uncertainty in Artificial Intelligence (UAI), Tel Aviv, Israel, 2019.

    PDF from arxiv.org

  3. L. M. Murray, D. Lundén, J. Kudlicka, D. Broman, and T. B. Schön. Delayed sampling and automatic Rao-Blackwellization of probabilistic programs. In International Conference on Artificial Intelligence and Statistics (AISTATS), pages 1037–1046, Playa Blanca, Lanzarote, Spain, 2018.

    PDF from arxiv.org

  4. J. Kudlicka, L. M. Murray, T. B. Schön, and F. Lindsten. Particle filter with rejection control and unbiased estimator of the marginal likelihood. In IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 5860–5864, 2020.

    PDF from arxiv.org