Incorporating Covariates into Integrated Factor Analysis of Multi-View Data

TL;DR

This paper introduces a supervised integrated factor analysis model that incorporates covariates for multi-view data, enabling better dimension reduction and interpretation in biomedical research.

Contribution

The paper develops a novel statistical model, SIFA, that decomposes multi-view data into joint and individual factors while integrating auxiliary covariates, with an efficient EM algorithm for fitting.

Findings

Applied to GTEx data, revealing new insights into gene expression variation.

Simulation studies show SIFA outperforms existing methods.

Demonstrated effectiveness in a pediatric growth study.

Abstract

In modern biomedical research, it is ubiquitous to have multiple data sets measured on the same set of samples from different views (i.e., multi-view data). For example, in genetic studies, multiple genomic data sets at different molecular levels or from different cell types are measured for a common set of individuals to investigate genetic regulation. Integration and reduction of multi-view data have the potential to leverage information in different data sets, and to reduce the magnitude and complexity of data for further statistical analysis and interpretation. In this paper, we develop a novel statistical model, called supervised integrated factor analysis (SIFA), for integrative dimension reduction of multi-view data while incorporating auxiliary covariates. The model decomposes data into joint and individual factors, capturing the joint variation across multiple data sets and the individual variation specific to each set respectively. Moreover, both joint and individual factors are partially informed by auxiliary covariates via nonparametric models. We devise a computationally efficient Expectation-Maximization (EM) algorithm to fit the model under some identifiability conditions. We apply the method to the Genotype-Tissue Expression (GTEx) data, and provide new insights into the variation decomposition of gene expression in multiple tissues. Extensive simulation studies and an additional application to a pediatric growth study demonstrate the advantage of the proposed method over competing methods.