On Semi-Supervised Estimation of Distributions

05/13/2023

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by   H. S. Melihcan Erol, et al.

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We study the problem of estimating the joint probability mass function (pmf) over two random variables. In particular, the estimation is based on the observation of m samples containing both variables and n samples missing one fixed variable. We adopt the minimax framework with l^p_p loss functions, and we show that the composition of uni-variate minimax estimators achieves minimax risk with the optimal first-order constant for p ≥ 2, in the regime m = o(n).