Spike-and-Slab Meets LASSO: A Review of the Spike-and-Slab LASSO

Bai, Ray; Ročková, Veronika; George, Edward I.

doi:10.1201/9781003089018-4

Cited by 21 publications

(11 citation statements)

References 60 publications

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“…Spike-and-slab LASSO (SSLASSO) was proposed by Ročková and George (2018) . It is based on the idea that every penalized likelihood has a Bayesian interpretation ( Bai et al, 2021 ). For instance, the LASSO penalization is equivalent to a Laplace distribution regulated by hyperparameter

, where the posterior mode of

is as follows:

…”

Section: Methodsmentioning

confidence: 99%

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Improvement of Genomic Predictions in Small Breeds by Construction of Genomic Relationship Matrix Through Variable Selection

et al. 2022

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Genomic selection has been increasingly implemented in the animal breeding industry, and it is becoming a routine method in many livestock breeding contexts. However, its use is still limited in several small-population local breeds, which are, nonetheless, an important source of genetic variability of great economic value. A major roadblock for their genomic selection is accuracy when population size is limited: to improve breeding value accuracy, variable selection models that assume heterogenous variance have been proposed over the last few years. However, while these models might outperform traditional and genomic predictions in terms of accuracy, they also carry a proportional increase of breeding value bias and dispersion. These mutual increases are especially striking when genomic selection is performed with a low number of phenotypes and high shrinkage value—which is precisely the situation that happens with small local breeds. In our study, we tested several alternative methods to improve the accuracy of genomic selection in a small population. First, we investigated the impact of using only a subset of informative markers regarding prediction accuracy, bias, and dispersion. We used different algorithms to select them, such as recursive feature eliminations, penalized regression, and XGBoost. We compared our results with the predictions of pedigree-based BLUP, single-step genomic BLUP, and weighted single-step genomic BLUP in different simulated populations obtained by combining various parameters in terms of number of QTLs and effective population size. We also investigated these approaches on a real data set belonging to the small local Rendena breed. Our results show that the accuracy of GBLUP in small-sized populations increased when performed with SNPs selected via variable selection methods both in simulated and real data sets. In addition, the use of variable selection models—especially those using XGBoost—in our real data set did not impact bias and the dispersion of estimated breeding values. We have discussed possible explanations for our results and how our study can help estimate breeding values for future genomic selection in small breeds.

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, where the posterior mode of

is as follows:

…”

Section: Methodsmentioning

confidence: 99%

“…The Bayesian prior can be rearranged in a penalized likelihood context by taking this marginal logarithm as a prior ( Bai et al, 2021 ); after some derivation, the following can be obtained:

where

…”

Section: Methodsmentioning

confidence: 99%

Improvement of Genomic Predictions in Small Breeds by Construction of Genomic Relationship Matrix Through Variable Selection

et al. 2022

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“…) such that a degenerate Dirac distribution about zero is chosen for the spike part. Point-mass priors have favorable statistical properties [e.g., Johnstone andSilverman, 2004, Castillo andvan der Vaart, 2012] but can be computationally prohibitive [Bai et al, 2021]. We hope to extend our algorithms to point-mass priors in follow-up work.…”

Section: For Linear Regression)mentioning

confidence: 99%

Scalable Spike-and-Slab

Biswas¹,

Mackey²,

Meng³

2022

Preprint

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Spike-and-slab priors are commonly used for Bayesian variable selection, due to their interpretability and favorable statistical properties. However, existing samplers for spikeand-slab posteriors incur prohibitive computational costs when the number of variables is large. In this article, we propose Scalable Spike-and-Slab (S 3 ), a scalable Gibbs sampling implementation for high-dimensional Bayesian regression with the continuous spike-and-slab prior of George and McCulloch [1993]. For a dataset with n observations and p covariates, S 3 has order max{n 2 pt, np} computational cost at iteration t where pt never exceeds the number of covariates switching spike-and-slab states between iterations t and t − 1 of the Markov chain. This improves upon the order n 2 p per-iteration cost of state-of-the-art implementations as, typically, pt is substantially smaller than p. We apply S 3 on synthetic and real-world datasets, demonstrating orders of magnitude speed-ups over existing exact samplers and significant gains in inferential quality over approximate samplers with comparable cost.

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“…To address this knowledge gap, two algorithms previously not used for clustering a groundwater geochemical dataset were selected; Gaussian finite mixture modeling (GFMM) (Scrucca et al 2016) and spike‐and‐slab Bayesian model (SSB) (Partovi Nia and Davison 2012). Successful applications of GFMM (e.g., Ellefsen et al 2014; Ellefsen and Smith 2016; Scrucca 2016; Marbac et al 2017; Popp et al 2019; Saranya et al 2020; Zhou and Wang 2020), and SSB (e.g., Tadesse et al 2005; Partovi Nia 2009; Partovi Nia and Davison 2012; Anderson and Vehtari 2017; Canale et al 2017; Cao et al 2019; Bai et al 2021), have been widely documented for datasets other than those relating to groundwater geochemistry.…”

Section: Introductionmentioning

confidence: 99%

Inspecting the Reliability of Geochemical Facies Identified for the Waterworks' Capture Zone in Germany

2022

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Little research attention has been given to validating clusters obtained from the groundwater geochemistry of the waterworks' capture zone with a prevailing lake-groundwater exchange. To address this knowledge gap, we proposed a new scheme whereby Gaussian finite mixture modeling (GFMM) and Spike-and-Slab Bayesian (SSB) algorithms were utilized to cluster the groundwater geochemistry while quantifying the probability of the resulting cluster membership against each other. We applied GFMM and SSB to 13 geochemical parameters collected during different sampling periods at 13 observation points across the Barnim Highlands plateau located in the northeast of Berlin, Germany; this included 10 observation wells, two lakes, and a gallery of drinking production wells. The cluster analysis of GFMM yielded nine clusters, either with a probability ≥0.8, while the SSB produced three hierarchical clusters with a probability of cluster membership varying from <0.2 to >0.8. The findings demonstrated that the clustering results of GFMM were in good agreement with the classification as per the principal component analysis and Piper diagram. By superimposing the parameter clustering onto the observation clustering, we could identify discrepancies that exist among the parameters of a certain cluster. This enables the identification of different factors that may control the geochemistry of a certain cluster, although parameters of that cluster share a strong similarity. The GFMM results have shown that from 2002, there has been active groundwater inflow from the lakes towards the capture zone. This means that it is necessary to adopt appropriate measures to reverse the inflow towards the lakes.

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Spike-and-Slab Meets LASSO: A Review of the Spike-and-Slab LASSO

Cited by 21 publications

References 60 publications

Improvement of Genomic Predictions in Small Breeds by Construction of Genomic Relationship Matrix Through Variable Selection

Improvement of Genomic Predictions in Small Breeds by Construction of Genomic Relationship Matrix Through Variable Selection

Scalable Spike-and-Slab

Inspecting the Reliability of Geochemical Facies Identified for the Waterworks' Capture Zone in Germany

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