An Adaptive Population Importance Sampler: Learning From Uncertainty

Martino, Luca; Elvira, Vı́ctor; Luengo, David; Corander, Jukka

doi:10.1109/tsp.2015.2440215

Cited by 71 publications

(81 citation statements)

References 41 publications

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“…In general, MIS strategies provide more robust algorithms, since they avoid entrusting the performance of the method to a single proposal. Moreover, many algorithms have been proposed in order to conveniently adapt the set of proposals in MIS [Cappé et al, 2004[Cappé et al, , 2008Martino et al, 2015a].…”

Section: Introductionmentioning

confidence: 99%

“…When a set of proposal pdfs is available, the way in which the samples can be drawn and weighted is not unique, unlike the case of using a single proposal. Indeed, different MIS algorithms in the literature (both adaptive and nonadaptive) have implicitly and independently interpreted the sampling and weighting procedures in different ways [Owen and Zhou, 2000;Cappé et al, 2004Cappé et al, , 2008Martino et al, 2015a;Cornuet et al, 2012;Bugallo et al, 2015]. Namely, there are several possible combinations of sampling and weighting schemes, when a set of proposal pdfs is available, which lead to valid MIS approximations of the target pdf.…”

Section: Introductionmentioning

confidence: 99%

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Generalized Multiple Importance Sampling

Elvira¹,

Martino²,

Luengo³

et al. 2019

Statist. Sci.

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104

121

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Importance sampling methods are broadly used to approximate posterior distributions or some of their moments. In its standard approach, samples are drawn from a single proposal distribution and weighted properly. However, since the performance depends on the mismatch between the targeted and the proposal distributions, several proposal densities are often employed for the generation of samples. Under this multiple importance sampling (MIS) scenario, many works have addressed the selection and adaptation of the proposal distributions, interpreting the sampling and the weighting steps in different ways. In this paper, we establish a novel general framework for sampling and weighting procedures when more than one proposal is available. The most relevant MIS schemes in the literature are encompassed within the new framework, and novel valid schemes appear naturally. All the MIS schemes are compared and ranked in terms of the variance of the associated estimators. Finally, we provide illustrative examples revealing that, even with a good choice of the proposal densities, a careful interpretation of the sampling and weighting procedures can make a significant difference in the performance of the method.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Generalized Multiple Importance Sampling

Elvira¹,

Martino²,

Luengo³

et al. 2019

Statist. Sci.

Self Cite

104

121

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show abstract

“…In adaptive IS algorithms, the proposals are iteratively adapted in order to reduce the mismatch w.r.t. the target (see for instance PMC [14], AMIS [15], or APIS [16]). However, this does not always occur, and a substantial mismatch can still remain in the first iterations even when the adaptation is successful (see for instance the discussion in [8,Section 4.2.]).…”

Section: Heretical Mismentioning

confidence: 99%

Heretical Multiple Importance Sampling

Elvira

Martino

Luengo

et al. 2016

IEEE Signal Process. Lett.

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Multiple Importance Sampling (MIS) methods approximate moments of complicated distributions by drawing samples from a set of proposal distributions. Several ways to compute the importance weights assigned to each sample have been recently proposed, with the so-called deterministic mixture (DM) weights providing the best performance in terms of variance, at the expense of an increase in the computational cost. A recent work has shown that it is possible to achieve a trade-off between variance reduction and computational effort by performing an a priori random clustering of the proposals (partial DM algorithm). In this paper, we propose a novel "heretical" MIS framework, where the clustering is performed a posteriori with the goal of reducing the variance of the importance sampling weights. This approach yields biased estimators with a potentially large reduction in variance. Numerical examples show that heretical MIS estimators can outperform, in terms of mean squared error (MSE), both the standard and the partial MIS estimators, achieving a performance close to that of DM with less computational cost.Comment: 8 pages, 2 figure

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“…The weighted samples are used to train the adapting sequence of distributions so that samples are drawn more efficiently as the iterations progress. The weighted samples form a sample from the posterior distribution under some mild conditions [30,37]. Ensemble importance sampling schemes also exist, e.g.…”

Section: Introductionmentioning

confidence: 99%

Ensemble Transport Adaptive Importance Sampling

Cotter

Russell³

2019

SIAM/ASA J. Uncertainty Quantification

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Markov chain Monte Carlo methods are a powerful and commonly used family of numerical methods for sampling from complex probability distributions. As applications of these methods increase in size and complexity, the need for efficient methods increases. In this paper, we present a particle ensemble algorithm. At each iteration, an importance sampling proposal distribution is formed using an ensemble of particles. A stratified sample is taken from this distribution and weighted under the posterior, a state-of-the-art ensemble transport resampling method is then used to create an evenly weighted sample ready for the next iteration. We demonstrate that this ensemble transport adaptive importance sampling (ETAIS) method outperforms MCMC methods with equivalent proposal distributions for low dimensional problems, and in fact shows better than linear improvements in convergence rates with respect to the number of ensemble members. We also introduce a new resampling strategy, multinomial transformation (MT), which while not as accurate as the ensemble transport resampler, is substantially less costly for large ensemble sizes, and can then be used in conjunction with ETAIS for complex problems. We also focus on how algorithmic parameters regarding the mixture proposal can be quickly tuned to optimise performance. In particular, we demonstrate this methodology's superior sampling for multimodal problems, such as those arising from inference for mixture models, and for problems with expensive likelihoods requiring the solution of a differential equation, for which speed-ups of orders of magnitude are demonstrated. Likelihood evaluations of the ensemble could be computed in a distributed manner, suggesting that this methodology is a good candidate for parallel Bayesian computations. allow us to sample from complex probability distributions which we would not be able to sample from directly. In particular, these methods have revolutionised the way in which inverse problems can be tackled, allowing full posterior sampling when using a Bayesian framework. However, this often comes at a very high cost, with a very large number of iterations required in order for the empirical approximation of the posterior to be considered good enough. As the cost of computing likelihoods can be extremely large, this means that many problems of interest are simply computationally intractable. This problem has been tackled in a variety of different ways. One approach is to construct increasingly complex MCMC methods which are able to use the structure of the posterior to make more intelligent proposals, leading to more thorough exploration of the posterior with fewer iterations. For example, the Hamiltonian or Hybrid Monte Carlo (HMC) algorithm uses gradient information and symplectic integrators in order to make very large moves in state with relatively high acceptance probabilities [43]. Non-reversible methods are also becoming quite popular as they can improve mixing [3]. Riemann manifold Monte Carlo methods exploit the Riemann geometry of t...

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An Adaptive Population Importance Sampler: Learning From Uncertainty

Cited by 71 publications

References 41 publications

Generalized Multiple Importance Sampling

Generalized Multiple Importance Sampling

Heretical Multiple Importance Sampling

Ensemble Transport Adaptive Importance Sampling

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