Sparse models for machine learning have received substantial attention over the past two decades. Model selection, or determining which features are the best explanatory variables, is critical to the interpretability of a learned model. Much of this work assumes that features are only mildly correlated. However, in modern applications ranging from functional MRI to genome-wide association studies, we observe highly correlated features that do not exhibit key properties (such as the restricted eigenvalue condition). In this talk, I will describe novel methods for robust sparse linear regression in these settings. Using side information about the strength of correlations among features, we form a graph with edge weights corresponding to pairwise correlations. This graph is used to define a graph total variation regularizer that promotes similar weights for highly correlated features. I will show how the graph structure encapsulated by this regularizer helps precondition correlated features to yield provably accurate estimates. The proposed approach outperforms several previous approaches in a variety of experiments on simulated and real fMRI data. This is joint work with Yuan Li, Ben Mark, and Garvesh Raskutti.

Rebecca Willett is a Professor of Statistics and Computer Science at the University of Chicago. Her research is focused on machine learning, signal processing, and large-scale data science. She completed her PhD in Electrical and Computer Engineering at Rice University in 2005 and was an Assistant then tenured Associate Professor of Electrical and Computer Engineering at Duke University from 2005 to 2013. She was an Associate Professor of Electrical and Computer Engineering, Harvey D. Spangler Faculty Scholar, and Fellow of the Wisconsin Institutes for Discovery at the University of Wisconsin-Madison from 2013 to 2018. Willett received the National Science Foundation CAREER Award in 2007, was a member of the DARPA Computer Science Study Group, and received an Air Force Office of Scientific Research Young Investigator Program award in 2010.