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Sparse probit linear mixed model. (English) Zbl 1460.62111

Summary: 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.

MSC:

62J05 Linear regression; mixed models
62J12 Generalized linear models (logistic models)
62F15 Bayesian inference
62R07 Statistical aspects of big data and data science
62P10 Applications of statistics to biology and medical sciences; meta analysis

Software:

Eigenstrat; DREBIN; ccSVM
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References:

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