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Poster
Multivariate f-divergence Estimation With Confidence
Kevin Moon · Alfred Hero

Wed Dec 10 04:00 PM -- 08:59 PM (PST) @ Level 2, room 210D #None

The problem of f-divergence estimation is important in the fields of machine learning, information theory, and statistics. While several divergence estimators exist, relatively few have known convergence properties. In particular, even for those estimators whose MSE convergence rates are known, the asymptotic distributions are unknown. We establish the asymptotic normality of a recently proposed ensemble estimator of f-divergence between two distributions from a finite number of samples. This estimator has MSE convergence rate of O(1/T), is simple to implement, and performs well in high dimensions. This theory enables us to perform divergence-based inference tasks such as testing equality of pairs of distributions based on empirical samples. We experimentally validate our theoretical results and, as an illustration, use them to empirically bound the best achievable classification error.

Author Information

Kevin Moon (Utah State University)
Alfred Hero (University of Michigan)