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Best Paper - Information-Theoretic Metric Learning

Description

In this paper, we present an information-theoretic approach to learning a Mahalanobis distance function. We formulate the problem as that of minimizing the differential relative entropy between two multivariate Gaussians under constraints on the distance function. We express this problem as a particular Bregman optimization problem: that of minimizing the LogDet divergence subject to linear constraints.

Our resulting algorithm has several advantages over existing methods.

First, our method can handle a wide variety of constraints and can optionally incorporate a prior on the distance function.

Second, it is fast and scalable. Unlike most existing methods, no eigenvalue computations or semi-definite programming are required.

We also present an online version and derive regret bounds for the resulting algorithm.

Finally, we evaluate our method on a recent error reporting system for software called Clarify, in the context of metric learning for nearest neighbor classification, as well as on standard data sets.

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