Sparse Probit Linear Mixed Model

TL;DR

This paper introduces the Sparse Probit Linear Mixed Model (Probit-LMM), a new method for feature selection and prediction in binary phenotypes that corrects for confounders and is scalable to high-dimensional data.

Contribution

The paper generalizes Linear Mixed Models to binary phenotypes using a Probit link and develops a scalable inference algorithm for high-dimensional data.

Findings

Improved prediction accuracy on real-world datasets.

Selected features with less correlation to confounders.

Effective handling of binary phenotypes in genetic studies.

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.