Adaptive Sampling for Estimating Probability Distributions

Jul 12, 2020



We consider the problem of allocating a fixed budget of samples to a finite set of discrete distributions to learn them uniformly well (minimizing the maximum error) in terms of four common distance measures: ℓ_2^2, ℓ_1, f-divergence, and separation distance. To present a unified treatment of these distances, we first propose a general optimistic tracking algorithm and analyze its sample allocation performance w.r.t. an oracle. We then instantiate this algorithm for the four distance measures and derive bounds on their regret. We also show that the allocation performance of the proposed algorithm cannot, in general, be improved, by deriving lower-bounds on the expected deviation from the oracle allocation for any adaptive scheme. We verify our theoretical findings through some experiments. Finally, we show that the techniques developed in the paper can be easily extended to learn some classes of continuous distributions as well as to the related setting of minimizing the average error (in terms of the four distances) in learning a set of distributions.



About ICML 2020

The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.

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