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Poster
Learning Low-Dimensional Metrics
Blake Mason · Lalit Jain · Robert Nowak

Tue Dec 05 06:30 PM -- 10:30 PM (PST) @ Pacific Ballroom #44
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This paper investigates the theoretical foundations of metric learning, focused on three key questions that are not fully addressed in prior work: 1) we consider learning general low-dimensional (low-rank) metrics as well as sparse metrics;2) we develop upper and lower (minimax) bounds on the generalization error; 3)we quantify the sample complexity of metric learning in terms of the dimension of the feature space and the dimension/rank of the underlying metric; 4) we also bound the accuracy of the learned metric relative to the underlying true generative metric. All the results involve novel mathematical approaches to the metric learning problem, and also shed new light on the special case of ordinal embedding (aka non-metric multidimensional scaling).

Keywords: Learning Theory · Similarity and Distance Learning · Metric Learning

Author Information

Blake Mason (University of Wisconsin - Madison)

Blake Mason is Doctoral Student at the University of Wisconsin-Madison studying Electrical and Computer Engineering under the advisement of Professor Robert Nowak. Prior to his graduate studies, he completed his bachelors in electrical engineering at the University of Southern California.

Lalit Jain (University of Michigan)
Robert Nowak (University of Wisconsion-Madison)

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