Sparse probit linear mixed model

Item Type:	Article
Title:	Sparse probit linear mixed model
Creators Name:	Mandt, S. and Wenzel, F. and Nakajima, S. and Cunningham, J. and Lippert, C. and Kloft, M.
Abstract:	Linear mixed models (LMMs) are important tools in statistical genetics. When used for feature selection, they allow to find a sparse set of genetic traits that best predict a continuous phenotype of interest, while simultaneously correcting for various confounding factors such as age, ethnicity and population structure. Formulated as models for linear regression, LMMs have been restricted to continuous phenotypes. We introduce the sparse probit linear mixed model (Probit-LMM), where we generalize the LMM modeling paradigm to binary phenotypes. As a technical challenge, the model no longer possesses a closed-form likelihood function. In this paper, we present a scalable approximate inference algorithm that lets us fit the model to high-dimensional data sets. We show on three real-world examples from different domains that in the setup of binary labels, our algorithm leads to better prediction accuracies and also selects features which show less correlation with the confounding factors.
Keywords:	Approximate Bayesian Inference, Feature Selection, Causality, Statistical Genetics
Source:	Machine Learning
ISSN:	0885-6125
Volume:	106
Number:	9-10
Page Range:	1621-1642
Date:	October 2017
Official Publication:	https://doi.org/10.1007/s10994-017-5652-6

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