On spike and slab empirical Bayes multiple testing

Castillo, Ismaël; Roquain, Étienne

doi:10.1214/19-aos1897

Cited by 24 publications

(73 citation statements)

References 40 publications

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“…In this setting control of the false discovery rate has been obtained recently for a knockoffs-based method in [34] and for an empirical Bayes method in [1]; in each case estimation of the HMM parameters is an essential first step. Modelling the proportion of non-null signals as vanishingly small, as our results permit, would allow for further links to the setting of sparse multiple testing, considered for example (with independent data) in [2,8].…”

Section: Related Workmentioning

confidence: 82%

Fundamental limits for learning hidden Markov model parameters

Abraham,

Naulet,

Gassiat

2021

Preprint

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We study the frontier between learnable and unlearnable hidden Markov models (HMMs). HMMs are flexible tools for clustering dependent data coming from unknown populations. The model parameters are known to be identifiable as soon as the clusters are distinct and the hidden chain is ergodic with a full rank transition matrix. In the limit as any one of these conditions fails, it becomes impossible to identify parameters. For a chain with two hidden states we prove nonasymptotic minimax upper and lower bounds, matching up to constants, which exhibit thresholds at which the parameters become learnable.Preprint. Under review.

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Section: Related Workmentioning

confidence: 82%

Fundamental limits for learning hidden Markov model parameters

Abraham,

Naulet,

Gassiat

2021

Preprint

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“…This is one of the most widely used approaches within the Bayesian community (Mitchell and Beauchamp 1988;George and McCulloch 1993;West 2003;Efron 2008) and includes the popular spike-and-slab prior, which is often considered the gold standard in sparse Bayesian linear regression. Such priors have been shown to perform well for estimation and prediction (Johnstone and Silverman 2004;Castillo and van der Vaart 2012;Castillo, Schmidt-Hieber, and van der Vaart 2015;Chae, Lin, and Dunson 2019), uncertainty quantification (Ray 2017;Castillo and Szabó 2020), and multiple hypothesis testing (Castillo and Roquain 2020), see Banerjee, Castillo, and Ghosal (2020) for a recent review. relaxation is significant, reducing the posterior dimension to a much more tractable O(p).…”

Section: Introductionmentioning

confidence: 99%

Variational Bayes for High-Dimensional Linear Regression With Sparse Priors

Ray

Szabó

2021

Journal of the American Statistical Association

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We study a mean-field spike and slab variational Bayes (VB) approximation to Bayesian model selection priors in sparse high-dimensional linear regression. Under compatibility conditions on the design matrix, oracle inequalities are derived for the mean-field VB approximation, implying that it converges to the sparse truth at the optimal rate and gives optimal prediction of the response vector. The empirical performance of our algorithm is studied, showing that it works comparably well as other state-of-the-art Bayesian variable selection methods. We also numerically demonstrate that the widely used coordinate-ascent variational inference algorithm can be highly sensitive to the parameter updating order, leading to potentially poor performance. To mitigate this, we propose a novel prioritized updating scheme that uses a data-driven updating order and performs better in simulations. The variational algorithm is implemented in the R package sparsevb. Supplementary materials for this article are available online.

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“…I tend to believe that both answers are positive. First it seems reasonable to think that the uniform FDR control can be proved by extending the methodology of Castillo and Roquain () to the bivariate case. Second, even with the uninformative Cauchy slab, the covariate T 2 can still help T 1 to make the correct decision, as illustrated in Fig.…”

Section: Discussion On the Paper By Cai Sun And Wangmentioning

confidence: 99%

Covariate-Assisted Ranking and Screening for Large-Scale Two-Sample Inference

Cai

Sun

Wang

2019

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary Two‐sample multiple testing has a wide range of applications. The conventional practice first reduces the original observations to a vector of p‐values and then chooses a cut‐off to adjust for multiplicity. However, this data reduction step could cause significant loss of information and thus lead to suboptimal testing procedures. We introduce a new framework for two‐sample multiple testing by incorporating a carefully constructed auxiliary variable in inference to improve the power. A data‐driven multiple‐testing procedure is developed by employing a covariate‐assisted ranking and screening (CARS) approach that optimally combines the information from both the primary and the auxiliary variables. The proposed CARS procedure is shown to be asymptotically valid and optimal for false discovery rate control. The procedure is implemented in the R package CARS. Numerical results confirm the effectiveness of CARS in false discovery rate control and show that it achieves substantial power gain over existing methods. CARS is also illustrated through an application to the analysis of a satellite imaging data set for supernova detection.

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On spike and slab empirical Bayes multiple testing

Cited by 24 publications

References 40 publications

Fundamental limits for learning hidden Markov model parameters

Fundamental limits for learning hidden Markov model parameters

Variational Bayes for High-Dimensional Linear Regression With Sparse Priors

Covariate-Assisted Ranking and Screening for Large-Scale Two-Sample Inference

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