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Learning Low-Dimensional Metrics

Presented by: 
Robert Nowak University of Wisconsin-Madison, Toyota Technological Institute
Tuesday 20th March 2018 - 09:00 to 10:00
INI Seminar Room 1
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). This is joint work with Lalit Jain and Blake Mason.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons