Elements of Sequential Monte Carlo

Naesseth, Christian A.; Lindsten, Fredrik; Schön, Thomas B.

doi:10.1561/9781680836332

Cited by 62 publications

(117 citation statements)

References 0 publications

Supporting

Mentioning

117

Contrasting

Order By: Relevance

“…We used inference algorithms in the SMC family, an option available in both WebPPL and Birch. An SMC algorithm 33 – 35 runs many simulations (called particles) in parallel, and stops them when some new information, like the time of a speciation event or extinction of a side lineage, becomes available. At such points, the particles are subjected to “resampling”, that is, sampling (with replacement) based on their likelihoods.…”

Section: Resultsmentioning

confidence: 99%

Universal probabilistic programming offers a powerful approach to statistical phylogenetics

et al. 2021

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Resultsmentioning

confidence: 99%

Universal probabilistic programming offers a powerful approach to statistical phylogenetics

et al. 2021

Self Cite

View full text Add to dashboard Cite

show abstract

“…We assume a basic understanding of SMC. For a complete introduction to SMC, we recommend Naesseth et al [26] and Doucet and Johansen [10].…”

Section: Formal Smcmentioning

confidence: 99%

“…Proof. As referenced in Naesseth et al [26], see Del Moral [7] Chopin [6][Theorem 1] gives another SMC convergence result in the form of a central limit. This result, however, requires further restrictions on the weights w j n in Algorithm 1.…”

Section: The Empirical Distributions {(A Jmentioning

confidence: 99%

See 1 more Smart Citation

Correctness of Sequential Monte Carlo Inference for Probabilistic Programming Languages

Lundén

Borgström

Broman

2021

Programming Languages and Systems

View full text Add to dashboard Cite

Probabilistic programming is an approach to reasoning under uncertainty by encoding inference problems as programs. In order to solve these inference problems, probabilistic programming languages (PPLs) employ different inference algorithms, such as sequential Monte Carlo (SMC), Markov chain Monte Carlo (MCMC), or variational methods. Existing research on such algorithms mainly concerns their implementation and efficiency, rather than the correctness of the algorithms themselves when applied in the context of expressive PPLs. To remedy this, we give a correctness proof for SMC methods in the context of an expressive PPL calculus, representative of popular PPLs such as WebPPL, Anglican, and Birch. Previous work have studied correctness of MCMC using an operational semantics, and correctness of SMC and MCMC in a denotational setting without term recursion. However, for SMC inference—one of the most commonly used algorithms in PPLs as of today—no formal correctness proof exists in an operational setting. In particular, an open question is if the resample locations in a probabilistic program affects the correctness of SMC. We solve this fundamental problem, and make four novel contributions: (i) we extend an untyped PPL lambda calculus and operational semantics to include explicit resample terms, expressing synchronization points in SMC inference; (ii) we prove, for the first time, that subject to mild restrictions, any placement of the explicit resample terms is valid for a generic form of SMC inference; (iii) as a result of (ii), our calculus benefits from classic results from the SMC literature: a law of large numbers and an unbiased estimate of the model evidence; and (iv) we formalize the bootstrap particle filter for the calculus and discuss how our results can be further extended to other SMC algorithms.

show abstract

“…For this reason, they are also referred to as “particle filters”. We refer the reader to [ 20 ] for the state-of-the-art of the early years and to the recent books [ 21 , 22 ] for pedagogical introductions and an overview of the most recent progress.…”

Section: Introductionmentioning

confidence: 99%