Compressed Particle Methods for Expensive Models With Application in Astronomy and Remote Sensing

Martino, Luca; Elvira, Vı́ctor; López‐Santiago, J.; Camps‐Valls, Gustau

doi:10.1109/taes.2021.3061791

Cited by 5 publications

(4 citation statements)

References 53 publications

(68 reference statements)

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“…Cappé et al (2008) use an entropy criterion instead to learn the weights and component parameters of a mixture IS density. Martino et al (2018Martino et al ( , 2021 compress MC representations, also by partitioning the space in disjoint sets and estimating the associated normalizing constants. Elvira et al (2015), Fasiolo et al (2018), andMousavi et al (2021) propose layered AIS schemes where the adaptation of the proposal is decoupled from the sampling steps.…”

Section: Related Workmentioning

confidence: 99%

Daisee: Adaptive importance sampling by balancing exploration and exploitation

Rainforth

Teh

2023

Scandinavian J Statistics

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We study adaptive importance sampling (AIS) as an online learning problem and argue for the importance of the trade‐off between exploration and exploitation in this adaptation. Borrowing ideas from the online learning literature, we propose Daisee, a partition‐based AIS algorithm. We further introduce a notion of regret for AIS and show that Daisee has cumulative pseudo‐regret, where is the number of iterations. We then extend Daisee to adaptively learn a hierarchical partitioning of the sample space for more efficient sampling and confirm the performance of both algorithms empirically.

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Section: Related Workmentioning

confidence: 99%

Daisee: Adaptive importance sampling by balancing exploration and exploitation

Rainforth

Teh

2023

Scandinavian J Statistics

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“…In [84], several compressing schemes are proposed and theoretically analyzed for assigned importance weights to groups of samples for distributed or decentralized Bayesian inference. The framework is extended in [73,74,86], where a stronger theoretical support is given, and new deterministic and random rules for compression are given. The approach in [60,6] considers the case of a single node that keeps simulating samples and assigning them an importance weight.…”

Section: Compressed and Distributed Ismentioning

confidence: 99%

Advances in Importance Sampling

Elvira

Martino

2021

Wiley StatsRef: Statistics Reference Online

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Importance sampling (IS) is a Monte Carlo technique for the approximation of intractable distributions and integrals with respect to them. The origin of IS dates from the early 1950s. In the last decades, the rise of the Bayesian paradigm and the increase of the available computational resources have propelled the interest in this theoretically sound methodology. In this paper, we first describe the basic IS algorithm and then revisit the recent advances in this methodology. We pay particular attention to two sophisticated lines. First, we focus on multiple IS (MIS), the case where more than one proposal is available. Second, we describe adaptive IS (AIS), the generic methodology for adapting one or more proposals.

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“…(Robert & Casella, 2004;Liu, 2004)), it is only now becoming more widespread. Nowadays, we can find applications of Bayesian inference methods in fields such as remote sensing (Martino, Elvira, et al, 2021;Llorente et al, 2021), astronomy (Feroz et al, 2019;Anfinogentov et al, 2021), cosmology (Ashton & Talbot, 2021;Ayuso et al, 2021), or optical spectroscopy (Emmert et al, 2019;Von Toussaint, 2011).…”

Section: Introductionmentioning

confidence: 99%

On the safe use of prior densities for Bayesian model selection

Llorente,

Martino,

Curbelo

et al. 2022

Preprint

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The application of Bayesian inference for the purpose of model selection is very popular nowadays. In this framework, models are compared through their marginal likelihoods, or their quotients, called Bayes factors. However, marginal likelihoods depends on the prior choice. For model selection, even diffuse priors can be actually very informative, unlike for the parameter estimation problem. Furthermore, when the prior is improper, the marginal likelihood of the corresponding model is undetermined. In this work, we discuss the issue of prior sensitivity of the marginal likelihood and its role in model selection. We also comment on the use of uninformative priors, which are very common choices in practice. Several practical suggestions are discussed and many possible solutions, proposed in the literature, to design objective priors for model selection are described. Some of them also allow the use of improper priors. The connection between the marginal likelihood approach and the well-known information criteria is also presented. We describe the main issues and possible solutions by illustrative numerical examples, providing also some related code. One of them involving a real-world application on exoplanet detection.

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Compressed Particle Methods for Expensive Models With Application in Astronomy and Remote Sensing

Cited by 5 publications

References 53 publications

Daisee: Adaptive importance sampling by balancing exploration and exploitation

Daisee: Adaptive importance sampling by balancing exploration and exploitation

Advances in Importance Sampling

On the safe use of prior densities for Bayesian model selection

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