Sharp Bounds for Generalized Uniformity Testing
Ilias Diakonikolas, Daniel M. Kane, Alistair Stewart
We study the problem of generalized uniformity testing of a discrete probability distribution: Given samples from a probability distribution p over an unknown size discrete domain Ω, we want to distinguish, with probability at least 2/ 3, between the case that p is uniform on some subset of Ω versus null -far, in total variation distance, from any such uniform distribution. We establish tight bounds on the sample complexity of generalized uniformity testing. In more detail, we present a computationally efficient tester whose sample complexity is optimal, within constant factors, and a matching worst-case information-theoretic lower bound.
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Manifold Structured Prediction
Structured prediction provides a general framework to deal with supervised problems where the outputs have semantically rich structure. While classical approaches consider finite, albeit potentially huge, output spaces, in this paper we discuss how structured prediction can be extended to a continuous scenario. Specifically, we study a structured prediction approach to manifold-valued regression. We characterize a class of problems for which the considered approach is statistically consistent and study how geometric optimization can be used to compute the corresponding estimator.
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