Sequential Monte Carlo samplers

By Pierre Del Moral, Arnaud Doucet. 2002

2,044 citations recorded by the source corpus.

Summary. We propose a methodology to sample sequentially from a sequence of probability distributions that are defined on a common space, each distribution being known up to a normalizing constant. These probability distributions are approximated by a cloud of weighted random samples which are propagated over time by using sequential Monte Carlo methods. This methodology allows us to derive simple algorithms to make parallel Markov chain Monte Carlo algorithms interact to perform global optimization and sequential Bayesian estimation and to compute ratios of normalizing constants. We illustrate these algorithms for various integration tasks arising in the context of Bayesian inference.

Subfields: Artificial Intelligence

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Citations in the corpus

Kernel Sequential Monte Carlo (2015, methodology): “In this paper, we focus on static SMC methods, which recently have generated increasing interest as an alternative to MCMC for Bayesian inference on a single target distribution [3, 4, 6, 11].”
Accurate and conservative estimates of MRF log-likelihood using reverse annealing (2014, methodology): “In particular, many algorithms, such as annealed importance sampling (Neal, 2001) and sequential Monte Carlo (del Moral et al., 2006), yield unbiased estimates ˆ Z tgt of the partition function, i.e. [ ˆ Z tgt ] = Z tgt .”
Venture: a higher-order probabilistic programming platform with programmable inference (2014, background): “Venture’s other inference programming instructions could be treated as rejuvenation kernels (Del Moral et al., 2006), and would not need to modify the weights7.”
Provable Bayesian Inference via Particle Mirror Descent (2015, methodology): “Sequential Monte-Carlo sampler [10] provides a unified view of SMC in Bayesian inference by adopting different forward/backward kernels, including the variants proposed in [8, 3] as special cases.”
Bayesian State-Space Modelling on High-Performance Hardware Using LibBi (2013, methodology): “The second approach is sequential Monte Carlo (SMC) [11].”
Quantifying the uncertainty in change points (2012, methodology): “SMC samplers (Del Moral et al., 2006) are a class of SMC algorithms in which a collection of auxiliary distributions are introduced to allow the SMC technique to be applied to essentially arbitrary sequences of distributions defined over any sequence of spaces.”
Optimization Monte Carlo: Efficient and Embarrassingly Parallel Likelihood-Free Inference (2015, methodology): “We focus our attention on population-based ABC samplers, which include rejection sampling, importance sampling (IS), sequential Monte Carlo (SMC) [6, 20] and population Monte Carlo [3].”
Monte Carlo Confidence Sets for Identified Sets (2016, background): “See Del Moral, Doucet, and Jasra (2012), Beskos, Jasra, Kantas, and Thiery (2016) and references therein for adaptive selection of tuning parameters with a SMC framework and theoretical analyses of the convergence properties of adaptive SMC algorithms.”
Delayed Sampling and Automatic Rao-Blackwellization of Probabilistic Programs (2017, positive): “This work focuses on Sequential Monte Carlo (SMC) inference algorithms [4], extending an arc of research that includes probabilistic programming languages (PPLs) such as Venture [14], Anglican [26], Probabilistic C [18], WebPPL [8], Fi-garo [20], and Turing [7], as well as similarly-motivated…”
Reinforcement learning with limited reinforcement: using Bayes risk for active learning in POMDPs (2008, neutral): “Indeed, because the model-uncertainty space is so large, and samples—models— are relatively expensive, a good proposal distribution is critical to our task [24].”
MCMC algorithms for Subset Simulation (2015, background): “It should be noted that Subset Simulation has been studied in the mathematical literature under the surrogate terms Sequential Monte Carlo (Del Moral et al. 2006, Cérou et al. 2012) and Generalized Splitting (Botev & Kroese 2012).”
ABC-EP: Expectation Propagation for Likelihoodfree Bayesian Computation (2011, methodology): “Del Moral et al. (2008) adapt sequential Monte Carlo techniques (Del Moral et al., 2006) to likelihood-free problems (ABC-SMC).”
Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems (2009, methodology): “Both algorithms are explained in detail in Del Moral et al. (2006). The disadvantage of the SMC sampler is that it is impossible to use an optimal backward kernel and it is hard to choose a good one.”
An Overview of Existing Methods and Recent Advances in Sequential Monte Carlo (2007, methodology): “It has now been recognised however that the use of sequential Monte Carlo methods offers some significant advantages over these non-sequential methods in certain cases [77], [78], [7].”