Sparse high-dimensional linea r regression and inverse problems have received su bstantial attention over the past two decades. Muc h of this work assumes that explanatory variables are only mildly correlated. However\, in modern ap plications ranging from functional MRI to genome-w ide association studies\, we observe highly correl ated explanatory variables and associated design m atrices that do not exhibit key properties (such a s the restricted eigenvalue condition). In this ta lk\, I will describe novel methods for robust spar se linear regression in these settings. Using side information about the strength of correlations am ong explanatory variables\, we form a graph with e dge weights corresponding to pairwise correlations . This graph is used to define a graph total varia tion regularizer that promotes similar weights for correlated explanatory variables. I will show how the graph structure encapsulated by this regulari zer interacts with correlated design matrices to y ield provably a ccurate estimates. The proposed ap proach outperforms standard methods in a variety o f experiments on simulated and real fMRI data.

This is joint work with Yuan Li and Ga rvesh Raskutti. LOCATION:Seminar Room 1\, Newton Institute CONTACT:INI IT END:VEVENT END:VCALENDAR