Dr. Jaroslaw Harezlak - Indiana U

Friday, March 20, 2020

2:00 - Maruey 115


Sparsity Inducing Nuclear-Norm Estimator (SpINNEr) for Matrix-Variate Regression - Brain Connectivity Analysis



Classical scalar-response linear models consider regressors in the form of a vector and estimate a corresponding vector of coefficients. In medical applications, however, covariates often appear as multi-dimensional arrays. For example, one may be interested in using Magnetic Resonance Imaging (MRI) to identify brain regions associated with a health outcome.

Vectorizing the two-dimensional image arrays is an unsatisfactory approach since it destroys the inherent spatial structure of the images and can be computationally challenging. We

propose an alternative approach, where the matrix of regression coefficients is found via a regularized regression. Our method, Sparsity Inducing Nuclear-Norm Estimator (SpINNEr), simultaneously imposes two penalty types on the regression coefficient matrix, the nuclear norm and the lasso norm, to encourage both a low rank and a sparse solution.

An implementation of the alternating direction method of multipliers (ADMM) is used to build a fast and efficient numerical solver. Our simulations show that SpINNEr outperforms other regularization methods in estimation accuracy when the response-related entries (representing the brain's functional connectivity) are arranged in well-connected communities. Finally, SpINNEr is applied to investigate associations between HIV-related outcomes and functional connectivity in the human brain.