Efficient Adaptive Multiple Importance Sampling

El-Laham, Yousef; Martino, Luca; Elvira, Vı́ctor; Bugallo, Mónica F.

doi:10.23919/eusipco.2019.8902642

Cited by 8 publications

(5 citation statements)

References 21 publications

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“…Moment-matching updates are often approximated through IS, as we do in Algorithm 2. Importance sampling estimation of π(Γ) or π (α) θ (Γ) is for instance used in the AMIS scheme of [27,64,38] for adaptive importance sampling, where proposals are constructed by matching the moments of the target. AMIS is recovered when α = 1, τ k ≡ 1 and r ≡ 0.…”

Section: Comparison With Existing Moment-matching Algorithmsmentioning

confidence: 99%

Regularized Rényi divergence minimization through Bregman proximal gradient algorithms

Guilmeau¹,

Chouzenoux²,

Elvira³

2022

Preprint

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We study the variational inference problem of minimizing a regularized Rényi divergence over an exponential family, and propose a relaxed moment-matching algorithm, which includes a proximal-like step. Using the information-geometric link between Bregman divergences and the Kullback-Leibler divergence, this algorithm is shown to be equivalent to a Bregman proximal gradient algorithm. This novel perspective allows us to exploit the geometry of our approximate model while using stochastic black-box updates. We use this point of view to prove strong convergence guarantees including monotonic decrease of the objective, convergence to a stationary point or to the minimizer, and convergence rates. These new theoretical insights lead to a versatile, robust, and competitive method, as illustrated by numerical experiments.

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Section: Comparison With Existing Moment-matching Algorithmsmentioning

confidence: 99%

Regularized Rényi divergence minimization through Bregman proximal gradient algorithms

Guilmeau¹,

Chouzenoux²,

Elvira³

2022

Preprint

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“…Since choosing a good proposal in advance is in general unfeasible, adaptive IS (AIS) methods adapt a mixture of proposals, iteratively improving the quality of the estimators by better fitting the proposals [3]. There are several families of AIS methods, such as the population Monte Carlo (PMC) [4]- [6], the AMIS algorithm [7], [8], or gradient-based techniques [9]- [11]. The research in AIS continues being very active and A. Mousavi and R. Monsefi are with Computer Department, Engineering Faculty, Ferdowsi University of Mashhad (FUM), Mashhad, Iran (e-mail: mousavi@iau-neyshabur.ac.ir; monsefi@um.ac.ir).…”

Section: Introductionmentioning

confidence: 99%

Hamiltonian Adaptive Importance Sampling

Mousavi

Monsefi

Elvira

2021

IEEE Signal Process. Lett.

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Importance sampling (IS) is a powerful Monte Carlo (MC) methodology for approximating integrals, for instance in the context of Bayesian inference. In IS, the samples are simulated from the so-called proposal distribution, and the choice of this proposal is key for achieving a high performance. In adaptive IS (AIS) methods, a set of proposals is iteratively improved. AIS is a relevant and timely methodology although many limitations remain yet to be overcome, e.g., the curse of dimensionality in high-dimensional and multi-modal problems. Moreover, the Hamiltonian Monte Carlo (HMC) algorithm has become increasingly popular in machine learning and statistics. HMC has several appealing features such as its exploratory behavior, especially in high-dimensional targets, when other methods suffer. In this paper, we introduce the novel Hamiltonian adaptive importance sampling (HAIS) method. HAIS implements a two-step adaptive process with parallel HMC chains that cooperate at each iteration. The proposed HAIS efficiently adapts a population of proposals, extracting the advantages of HMC. HAIS can be understood as a particular instance of the generic layered AIS family with an additional resampling step. HAIS achieves a significant performance improvement in high-dimensional problems w.r.t. state-of-the-art algorithms. We discuss the statistical properties of HAIS and show its high performance in two challenging examples.

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“…Moreover, in the lower layer, the cost of weighting can be quite high if we have run long MCMC chains in the upper layer. This problem can also be alleviated by using ideas such as compression or alternative weighting schemes, that reduce the cost but maintain the same performance for the final estimators [11,12,13].…”

Section: Introductionmentioning

confidence: 99%

MCMC-driven importance samplers

Llorente,

Curbelo,

Martino

et al. 2021

Preprint

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Monte Carlo methods are the standard procedure for estimating complicated integrals of multidimensional posterior distributions in Bayesian inference. In this work, we focus on LAIS, a class of adaptive importance samplers where Markov chain Monte Carlo (MCMC) algorithms are employed to drive an underlying multiple importance sampling (IS) scheme. Its power lies in the simplicity of the layered framework: the upper layer locates proposal densities by means of MCMC algorithms, whereas the lower layer handles the multiple IS scheme, in order to compute the final estimators. The modular nature of LAIS allows for different possible choices in the upper and lower layers, yielding a variety of different performance and computational costs. In this work, we propose different enhancements in order to increase the efficiency and reduce the computational cost, of both upper and lower layers. The different variants are essential if we aim to address computational challenges arising in real-world applications, such as highly concentrated posterior distributions (due to large amounts of data, etc.). Hamiltonian-driven importance samplers are presented and tested. Furthermore, we introduce different strategies for designing cheaper schemes, for instance, recycling samples generated in the upper layer and using them in the final estimators in the lower layer. Numerical experiments show the benefits of the proposed schemes as compared to vanilla version of LAIS and other benchmark methods.

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Efficient Adaptive Multiple Importance Sampling

Cited by 8 publications

References 21 publications

Regularized Rényi divergence minimization through Bregman proximal gradient algorithms

Regularized Rényi divergence minimization through Bregman proximal gradient algorithms

Hamiltonian Adaptive Importance Sampling

MCMC-driven importance samplers

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