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arXiv · 1605.09124

Minimax Rate-Optimal Estimation of Divergences between Discrete Distributions

Yanjun Han·Jiantao Jiao·Tsachy Weissman
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Abstract

We study the minimax estimation of $\alpha$-divergences between discrete distributions for integer $\alpha\ge 1$, which include the Kullback--Leibler divergence and the $\chi^2$-divergences as special examples. Dropping the usual theoretical tricks to acquire independence, we construct the first minimax rate-optimal estimator which does not require any Poissonization, sample splitting, or explicit construction of approximating polynomials. The estimator uses a hybrid approach which solves a problem-independent linear program based on moment matching in the non-smooth regime, and applies a problem-dependent bias-corrected plug-in estimator in the smooth regime, with a soft decision boundary between these regimes.

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Yanjun Han, Jiantao Jiao, Tsachy Weissman. 2016-05-30. Minimax Rate-Optimal Estimation of Divergences between Discrete Distributions. https://doi.org/10.1109/jsait.2020.3041036

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