Incorporating prior information and borrowing information in high-dimensional sparse regression using the horseshoe and variational Bayes

2019/01/29 by Gino B. Kpogbezan, Kpogbezan, Gino B., Mark A. van de Wiel +6
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Gene expression and cancer classification #Statistical Methods and Inference #stat.ME

paper · pdf · doi:10.48550/arxiv.1901.10217

arxiv created 2019/01/29 · arxiv updated 2019/01/30

Abstract

We introduce a sparse high-dimensional regression approach that can incorporate prior information on the regression parameters and can borrow information across a set of similar datasets. Prior information may for instance come from previous studies or genomic databases, and information borrowed across a set of genes or genomic networks. The approach is based on prior modelling of the regression parameters using the horseshoe prior, with a prior on the sparsity index that depends on external information. Multiple datasets are integrated by applying an empirical Bayes strategy on hyperparameters. For computational efficiency we approximate the posterior distribution using a variational Bayes method. The proposed framework is useful for analysing large-scale data sets with complex dependence structures. We illustrate this by applications to the reconstruction of gene regulatory networks and to eQTL mapping.

Citations

• The horseshoe estimator for sparse signals

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