Joint estimation of sparse multivariate regression and conditional graphical models
This work addresses the need for efficient modeling of dependencies in multivariate responses for applications like cancer data analysis, representing an incremental improvement over existing sparse regression techniques.
The authors tackled the problem of high-dimensional multivariate regression by proposing a method that jointly estimates sparse regression coefficients and conditional graphical structures, achieving asymptotic selection consistency and normality for diverging dimensions.
Multivariate regression model is a natural generalization of the classical univari- ate regression model for fitting multiple responses. In this paper, we propose a high- dimensional multivariate conditional regression model for constructing sparse estimates of the multivariate regression coefficient matrix that accounts for the dependency struc- ture among the multiple responses. The proposed method decomposes the multivariate regression problem into a series of penalized conditional log-likelihood of each response conditioned on the covariates and other responses. It allows simultaneous estimation of the sparse regression coefficient matrix and the sparse inverse covariance matrix. The asymptotic selection consistency and normality are established for the diverging dimension of the covariates and number of responses. The effectiveness of the pro- posed method is also demonstrated in a variety of simulated examples as well as an application to the Glioblastoma multiforme cancer data.