Adaptive Multiple Importance Sampling

By Jean-Marie Cornuet, Jean-Michel Marin, Antonietta Mira, Christian P. Robert. 2009

286 citations recorded by the source corpus.

Abstract. The Adaptive Multiple Importance Sampling algorithm is aimed at an optimal recycling of past simulations in an iterated importance sampling (IS) scheme. The difference with earlier adaptive IS implementations like Population Monte Carlo is that the importance weights of all simulated values, past as well as present, are recomputed at each iteration, following the technique of the deterministic multiple mixture estimator of Owen & Zhou (J. Amer. Statist. Assoc., 95, 2000, 135). Although the convergence properties of the algorithm cannot be investigated, we demonstrate through a challenging banana shape target distribution and a population genetics example that the improvement brought by this technique is substantial.

Subfields: Artificial Intelligence, Statistics and Probability

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Citations in the corpus

Control functionals for Monte Carlo integration (2014, methodology): “These include (a) importance sampling and its extensions (Cornuet et al., 2012; Li et al., 2013), (b) stratified sampling and related techniques (Rubinstein and Kroese, 2011), (c) antithetic variables (Green and Han, 1992) and more generally (randomized) quasi- Monte-Carlo (RQMC) sampling (Dick and…”
Efficient MCMC for Climate Model Parameter Estimation: Parallel Adaptive Chains and Early Rejection (2012, background): “Novel ways to implement importance sampling, such as the adaptive multiple importance sampling (AMIS) algorithm of Cornuet et al. (2012), could help, but this question is out of the scope of this paper.”
Expectation Propagation as a Way of Life (2020, methodology): “Another approach, which can be used in serial or parallel EP, is to use adaptive multiple importance sampling (Cornuet et al., 2012), which would make it possible to recycle the simulations from previous iterations.”
Expectation Propagation as a Way of Life: A Framework for Bayesian Inference on Partitioned Data (2014, methodology): “Another approach, which can be used in serial or parallel EP, is to use adaptive multiple importance sampling (Cornuet et al., 2012), which would make it possible to recycle the simulations from previous iterations.”
MCMC-Driven Adaptive Multiple Importance Sampling (2015, methodology): “The population Monte Carlo (PMC) [2] and the adaptive multiple importance sampling (AMIS) [3] methods are two general schemes that combine the proposal adaptation idea with the cooperative use of a population of different proposal pdfs.”
Pareto Smoothed Importance Sampling (2015, methodology): “In this paper we focus on the case with a fixed proposal distribution, but the presented method can also be used as part of sequential, iterative and adaptive importance sampling (e.g. Kong et al., 1994; Owen and Zhou, 2000; Raftery and Bao, 2010; Bornn et al., 2010; Cornuet et al., 2012; Owen, 2013”
Generalized Multiple Importance Sampling (2015, methodology): “Several algorithms have been proposed in the last decade (Cappé et al., 2008; Cornuet et al., 2012; Martino et al., 2015a, 2017; Elvira et al., 2017).”
ZhuSuan: A Library for Bayesian Deep Learning (2017, background): “Therefore people have been exploring the use of adaptive proposals (Capp´e et al., 2008; Cornuet et al., 2012).”
Gradient Importance Sampling (2015, unknown): “A particularly interesting approach is Adaptive Multiple Importance Sampling [18, 19].”
Importance Nested Sampling and the MultiNest Algorithm (2013, background): “…to ensure that a limiting distribution exists (this echoes the requirement for there to exist an optimal proposal in the equivalent AMIS analysis of Marin et al. 2012), and to ensure that its form is such as to render irrelevant the inevitable stochastic variation and bias in our negative binomial…”