Robert Nowak: Learning Low-Dimensional Metrics

Mon, May 14, 2018, 12:30 pm
Sherrerd Hall 101


Abstract: This talk discusses the problem of learning a low-dimensional Euclidean metric from distance comparisons. Specifically, consider a set of n items with high-dimensional features and suppose we are given a set of (possibly noisy) distance comparisons of the form sign(dist(x,y) − dist(x,z)), where x, y, and z are the features associated with three such items. The goal is to learn the distance function that generates such comparisons. The talk focuses on several key issues pertaining to the theoretical foundations of metric learning: 1) optimization methods for learning general low-dimensional (low-rank) metrics as well as sparse metrics; 2) upper and lower (minimax) bounds on prediction error; 3) quantification of the sample complexity of metric learning in terms of the dimension of the feature space and the dimension/rank of the underlying metric; 4) bounds on the accuracy of the learned metric relative to the underlying true generative metric. Our results involve novel mathematical approaches to the metric learning problem and shed new light on the special case of ordinal embedding (aka non-metric multidimensional scaling).

Bio: Rob is the McFarland-Bascom Professor in Engineering at the University of Wisconsin-Madison, where his research focuses on signal processing, machine learning, optimization, and statistics.

Seminar is co-sponsored by CSML and S. S. Wilks Memorial Seminar in Statistics