Empirical Bayesian elastic net for multiple quantitative trait locus mapping

Huang, Anhui; Xu, Shizhong; Cai, Xiaodong

doi:10.1038/hdy.2014.79

Cited by 29 publications

(29 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Conversely marginal posterior estimates (i.e., MMAP) of θ followed by joint posterior modal inference of g (and β) conditional on MMAP(θ) are typical of a more stable EBbased approach to inference with hierarchical models, similar to using REML followed by BLUP (Robinson 1991). Other researchers have taken yet a completely different approach by treating elements of θ as if they were augmented variables whose uncertainty is accounted for by integrating them out of the joint posterior density, whereas SNP-specific variances (i.e., τ) are considered as parameters to be estimated (Cai et al 2011;Huang et al 2015;Xu 2007). Given that each element of τ defines the relative variance of a single element of g, we are not sure that this is particularly advisable; nevertheless, more rigorous comparisons of their approach with our proposed strategy may be warranted.…”

Section: Discussionmentioning

confidence: 99%

An Integrated Approach to Empirical Bayesian Whole Genome Prediction Modeling

Chen

Tempelman

2015

JABES

View full text Add to dashboard Cite

Computational efficiency is an increasing concern for whole genome prediction (WGP) based on denser genetic marker panels such that algorithms other than Markov Chain Monte Carlo (MCMC) warrant greater consideration, particularly for hierarchical models that flexibly confer either heavy-tailed (e.g., BayesA) or stochastic search and variable selection (SSVS) instead of Gaussian specifications on marker effect distributions. The expectation maximization (EM) algorithm is one attractive alternative; however, recently proposed hierarchical model implementations of EM have not addressed formal estimation of underlying hyperparameters even though their specifications are known to impact WGP accuracy. Furthermore, EM can be sensitive to starting values. We develop and explore the properties of an empirical Bayes strategy by conditioning EM implementations of BayesA or SSVS WGP models on marginal modal estimation of variance components and other key hyperparameters. These empirical Bayes implementations are compared against their MCMC counterparts for estimation of hyperparameters and WGP accuracy, both within the context of a simulation study and application to a loblolly pine dataset. In all cases, starting values were deemed to be important for EM-based estimates. Starting values based on MCMC posterior means were preferable, whereas those based on setting all marker effects equal to zero generally led to inferior performance. Nevertheless, a recently proposed regularization procedure was useful in alleviating the impact of starting values in the EM implementation of the SSVS model, as was modifying the expectation step in the BayesA model to be based on relative variances rather than on relative precisions.

show abstract

Section: Discussionmentioning

confidence: 99%

An Integrated Approach to Empirical Bayesian Whole Genome Prediction Modeling

Chen

Tempelman

2015

JABES

View full text Add to dashboard Cite

show abstract

“…For example, both EBlasso-NEG [12,13] and our recent developed EBEN [14] have more parameters and require much more computation in cross validation to identify their optimal values. It will be very useful to have more efficient proximal algorithms for these methods.…”

Section: Discussionmentioning

confidence: 99%

“…Recently we developed an efficient empirical Bayesian Lasso (EBlasso) algorithm using a two-level hierarchical model with normal and exponential priors (EBlasso-NE) or a three-level hierarchical model with normal, exponential, and Gamma priors (EBlasso-NEG) [12,13], and an empirical Bayesian elastic net (EBEN) using a two-level hierarchical model with normal and generalized gamma priors [14] for multiple QTL mapping. Both EBlasso and EBEN outperform other shrinkage methods including Lasso and MCMC-based Bayesian shrinkage methods in terms of PD and FDR.…”

Section: Introductionmentioning

confidence: 99%

Fast proximal gradient optimization of the empirical Bayesian Lasso for multiple quantitative trait locus mapping

Appuhamilage

Huang

Cai

2014

2014 IEEE Global Conference on Signal and Information Processing (GlobalSIP)

View full text Add to dashboard Cite

Complex quantitative traits are influenced by many factors including the main effects of many quantitative trait loci (QTLs), the epistatic effects involving more than one QTLs, environmental effects and the effects of gene-environment interactions. We recently developed an empirical Bayesian Lasso (EBlasso) method that employs a high-dimensional sparse regression model to infer the QTL effects from a large set of possible effects. Although EBlasso outperformed other state-ofthe-art algorithms in terms of power of detection (PD) and false discovery rate (FDR), it was optimized by a greedy coordinate ascent algorithm that limited its capability and efficiency in handling a relatively large number of possible QTLs. In this paper, we developed a fast proximal gradient optimization algorithm for the EBlasso method. The new algorithm inherits the accuracy of our previously developed coordinate ascent algorithm, and achieves much faster computational speed. Simulation results demonstrated that the proximal gradient algorithm provided better PD with the same FDR as the coordinate ascent algorithm, and computational time was reduced by more than 30%. The proximal gradient algorithm enhanced EBlasso will be a useful tool for multiple QTL mappings especially when there are a large number of possible effects. A C/C++ software implementing the proximal gradient algorithm is freely available upon request.I.

show abstract

“…Thus, the problem of variable selection reduces to the identification of the nonzero regression coefficients (Alhamzawi and Taha Mohammad Ali (2018)). Especially shrinkage approaches such as the lasso (Tibshirani (1996)), the adaptive lasso (Zou (2006)), the elastic net (Zou and Hastie (2005)) and their Bayesian analogues (Park and Casella (2008); Alhamzawi et al (2012); Leng et al (2014); Huang et al (2015)) which simultaneously perform variable selection and coefficient estimation have been shown to be effective and are often the methods of choice in linear regression. These methods estimate β as minimizer of the objective function L(β)+P (β, λ), where L denotes the quadratic loss function (negative log-likelihood) n i=1 (y i −x T i β) 2 and P denotes a method specific penalty function that encourages a sparse solution.…”

Section: Introductionmentioning

confidence: 99%

A novel Bayesian approach for variable selection in linear regression models

Posch

Arbeiter

Pilz

2020

Computational Statistics & Data Analysis

View full text Add to dashboard Cite

We propose a novel Bayesian approach to the problem of variable selection in multiple linear regression models. In particular, we present a hierarchical setting which allows for direct specification of a-priori beliefs about the number of nonzero regression coefficients as well as a specification of beliefs that given coefficients are nonzero. To guarantee numerical stability, we adopt a g-prior with an additional ridge parameter for the unknown regression coefficients. In order to simulate from the joint posterior distribution an intelligent random walk Metropolis-Hastings algorithm which is able to switch between different models is proposed. Testing our algorithm on real and simulated data illustrates that it performs at least on par and often even better than other well-established methods. Finally, we prove that under some nominal assumptions, the presented approach is consistent in terms of model selection. 45However, the g-prior depends on the inverse of the empirical covariance matrix of the selected predictors. This matrix is singular if the number of selected covariates is greater than the number of observations n and, further, may be almost rank deficient given that the predictors are highly correlated. To overcome this problem Wang et al. (2015) replaced the classical inverse with the Moore-Penrose generalized inverse and thus ended up with the so-called gsg-prior (see West (2003)). In contrast to them, we adopt a g-prior 50 with an additional ridge parameter for the unknown regression coefficients to guarantee nonsingularity of the empirical covariance matrix. This modification of the classical g-prior was first proposed by Gupta and Ibrahim (2007) and further investigated by Baragatti and Pommeret (2012).Finally, in Section 2.2 we state that our approach is consistent in terms of model selection according to the consistency definition given by Fernández et al. (2001). The proof of this result is deferred to the 55 appendix. Moreover, in Section 3, we evaluate our approach on the basis of real and simulated data and compare the results with the already described shrinkage methods. We show that our approach performs at least on par and often better than the comparative methods.

show abstract

Empirical Bayesian elastic net for multiple quantitative trait locus mapping

Cited by 29 publications

References 32 publications

An Integrated Approach to Empirical Bayesian Whole Genome Prediction Modeling

An Integrated Approach to Empirical Bayesian Whole Genome Prediction Modeling

Fast proximal gradient optimization of the empirical Bayesian Lasso for multiple quantitative trait locus mapping

A novel Bayesian approach for variable selection in linear regression models

Contact Info

Product

Resources

About