Enforcing Co-expression in Multimodal Regression Framework

We consider the problem of multimodal data integration for the study of complex neurological diseases (e.g. schizophrenia). Among the challenges arising in such situation, estimating the link between genetic and neurological variability within a population sample has been a promising direction. A wide variety of statistical models arose from such applications. For example, Lasso regression and its multitask extension are often used to fit a multivariate linear relationship between given phenotype(s) and associated observations. Other approaches, such as canonical correlation analysis (CCA), are widely used to extract relationships between sets of variables from different modalities. In this paper, we propose an exploratory multivariate method combining these two methods. More Specifically, we rely on a 'CCA-type' formulation in order to regularize the classical multimodal Lasso regression problem. The underlying motivation is to extract discriminative variables that display are also co-expressed across modalities. We first evaluate the method on a simulated dataset, and further validate it using Single Nucleotide Polymorphisms (SNP) and functional Magnetic Resonance Imaging (fMRI) data for the study of schizophrenia.