Abstract: Multi-modal data are prevalent in many scientific fields. In this study, we consider the parameter estimation and variable selection for a multi-response regression using block-missing multi-modal data. Our method allows the dimensions of both the responses and the predictors to be large, and the responses to be incomplete and correlated, a common practical problem in high-dimensional settings. Our proposed method uses two steps to make a prediction from a multi-response linear regression model with block-missing multi-modal predictors. In the first step, without imputing missing data, we use all available data to estimate the covariance matrix of the predictors and the cross-covariance matrix between the predictors and the responses. In the second step, we use these matrices and a penalized method to simultaneously estimate the precision matrix of the response vector, given the predictors, and the sparse regression parameter matrix. Lastly, we demonstrate the effectiveness of the proposed method using theoretical studies, simulated examples, and an analysis of a multi-modal imaging data set from the Alzheimer's Disease Neuroimaging Initiative.

Key words and phrases: Inverse covariance matrix estimation, Lasso, missing data, moment estimation.