  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.
