QTL Mapping Using a Memetic Algorithm with Modifications of BIC as Fitness Function

Frommlet, Florian; Ljubić, Ivana; Arnardóttir, Helga Björk; Bogdan, Małgorzata

doi:10.1515/1544-6115.1793

Cited by 7 publications

(7 citation statements)

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“…Yet another approach for Bayesian model selection is addressed by Bottolo et al (2011), who propose the moves of MCMC between local optima through a permutation based genetic algorithm that has a pool of solutions in a current generation suggested by parallel tempered chains. A similar idea is considered by Frommlet et al (2012). Multiple try MCMC methods with local optimization have been described by Liu et al (2000).…”

Section: Introductionmentioning

confidence: 99%

Mode jumping MCMC for Bayesian variable selection in GLMM

Hubin

Storvik

2018

Computational Statistics & Data Analysis

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Generalized linear mixed models (GLMM) are used for inference and prediction in a wide range of different applications providing a powerful scientific tool. An increasing number of sources of data are becoming available, introducing a variety of candidate explanatory variables for these models. Selection of an optimal combination of variables is thus becoming crucial. In a Bayesian setting, the posterior distribution of the models, based on the observed data, can be viewed as a relevant measure for the model evidence. The number of possible models increases exponentially in the number of candidate variables. Moreover, the space of models has numerous local extrema in terms of posterior model probabilities. To resolve these issues a novel MCMC algorithm for the search through the model space via efficient mode jumping for GLMMs is introduced. The algorithm is based on 1 The corresponding author, Aliaksandr Hubin, is a PhD candidate at the University of Oslo, 0851 Moltke Moes vei 35 Oslo, Norway. Email: aliaksah@math.uio.no, tel: +4745171361. The paper has supplementary materials consisting of: R package: R package EMJMCMC to perform the efficient mode jumping MCMC described in the paper. (EMJMCMC 1.2.tar.gz; GNU zipped tar file). Data and code: Data (simulated and real) and R code for MJMCMC algorithm, postprocessing and creating figures wrapped together into a reference based EMJMCMC class.(code-and-data.zip; zip file containing the data, code and a read-me file (readme.pdf)) Details and Pseudo code: Proofs of the ergodicity of MJMCMC procedure, pseudo codes for MJMCMC and local combinatorial optimizers, parallelization strategies and some supplementary tables for the experiments. (appendix.pdf) that marginal likelihoods can be efficiently calculated within each model. It is recommended that either exact expressions or precise approximations of marginal likelihoods are applied. The suggested algorithm is applied to simulated data, the famous U.S. crime data, protein activity data and epigenetic data and is compared to several existing approaches.

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Section: Introductionmentioning

confidence: 99%

Mode jumping MCMC for Bayesian variable selection in GLMM

Hubin

Storvik

2018

Computational Statistics & Data Analysis

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“…Our heuristic search strategy is attempting to get close to the global minimum, but we know that in most cases it will fail to find the best solution. More involved search strategies will further improve our method, and we are currently exploring the use of memetic algorithms, which have been successfully applied already in the context of QTL mapping [22] .…”

Section: Discussionmentioning

confidence: 99%

Analyzing Genome-Wide Association Studies with an FDR Controlling Modification of the Bayesian Information Criterion

Dolejsi

Bodenstorfer²,

Frommlet

2014

PLoS ONE

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The prevailing method of analyzing GWAS data is still to test each marker individually, although from a statistical point of view it is quite obvious that in case of complex traits such single marker tests are not ideal. Recently several model selection approaches for GWAS have been suggested, most of them based on LASSO-type procedures. Here we will discuss an alternative model selection approach which is based on a modification of the Bayesian Information Criterion (mBIC2) which was previously shown to have certain asymptotic optimality properties in terms of minimizing the misclassification error. Heuristic search strategies are introduced which attempt to find the model which minimizes mBIC2, and which are efficient enough to allow the analysis of GWAS data. Our approach is implemented in a software package called MOSGWA. Its performance in case control GWAS is compared with the two algorithms HLASSO and d-GWASelect, as well as with single marker tests, where we performed a simulation study based on real SNP data from the POPRES sample. Our results show that MOSGWA performs slightly better than HLASSO, where specifically for more complex models MOSGWA is more powerful with only a slight increase in Type I error. On the other hand according to our simulations GWASelect does not at all control the type I error when used to automatically determine the number of important SNPs. We also reanalyze the GWAS data from the Wellcome Trust Case-Control Consortium and compare the findings of the different procedures, where MOSGWA detects for complex diseases a number of interesting SNPs which are not found by other methods.

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“…Here L is the number of layers, p (l) is the number of nodes within the layer while σ In our notation we explicitly differentiate between discrete model configurations defined by the vectors γ = {γ (l) kj , j = 1, .., p (l+1) , k = 0, ..., p (l) , l = 1, ..., L} (further referred to as models) constituting the model space Γ and parameters of the models, conditional on these configurations θ|γ = {β, φ|γ}, where only those β (l) kj for which γ (l) kj = 1 are included. This approach is a rather standard (in statistical science literature) way to explicitly specify the model uncertainty in a given class of models and is used in Clyde et al (2011), Frommlet et al (2012, Hubin & Storvik (2018), Hubin et al (2018b,a). A Bayesian approach is obtained by specification of model priors p(γ) and parameter priors for each model p(β|γ).…”

Section: The Modelmentioning

confidence: 99%

“…At the same time pruning is done in an implicit manner by deleting the weights via ad-hoc thresholding. In Bayesian model selection problems there have been numerous works showing efficiency and accuracy of model selection by means of introducing latent variables corresponding to different discrete model configurations, and then conditioning on their marginal posterior to both select the best sparse configuration and address the joint model-and-parameters-uncertainty explicitly (George & McCulloch 1993, Clyde et al 2011, Frommlet et al 2012, Hubin & Storvik 2018, Hubin et al 2018b. For instance, Hubin et al (2018a) address inference in the class of deep Bayesian regression models (DBRM), which generalizes the class of Bayesian neural networks.…”

Section: Introductionmentioning

confidence: 99%

Combining Model and Parameter Uncertainty in Bayesian Neural Networks

Hubin¹,

Storvik²

2019

Preprint

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Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using Bayesian approach: Parameter and prediction uncertainty become easily available, facilitating rigid statistical analysis. Furthermore, prior knowledge can be incorporated. However so far there have been no scalable techniques capable of combining both model (structural) and parameter uncertainty. In this paper we introduce the concept of model uncertainty in BNNs and hence make inference in the joint space of models and parameters. Moreover, we suggest an adaptation of a scalable variational inference approach with reparametrization of marginal inclusion probabilities to incorporate the model space constraints. Finally, we show that incorporating model uncertainty via Bayesian model averaging and Bayesian model selection allows to drastically sparsify the structure of BNNs.Preprint. Under review.

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QTL Mapping Using a Memetic Algorithm with Modifications of BIC as Fitness Function

Cited by 7 publications

References 0 publications

Mode jumping MCMC for Bayesian variable selection in GLMM

Mode jumping MCMC for Bayesian variable selection in GLMM

Analyzing Genome-Wide Association Studies with an FDR Controlling Modification of the Bayesian Information Criterion

Combining Model and Parameter Uncertainty in Bayesian Neural Networks

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