Minimax Estimation of Discrete Distributions under ℓ1 Loss

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Learning discrete distributions: user vs item-level privacy (2020, background): “…privacy has been studied extensively with various loss functions and non-asymptotic convergence rates [Braess and Sauer, 2004, Kamath et al., 2015, Han et al., 2015], with local diﬀerential privacy [Duchi et al., 2013, Kairouz et al., 2016, Acharya et al., 2019a, Ye and Barg, 2018], with global…”
Formal Limitations on the Measurement of Mutual Information (2018, background): “Past work on analyzing minimax bounds likewise assume small support (Jiao et al., 2015; Han et al., 2015; Kandasamy et al., 2015).”
Maximum Likelihood Estimation of Functionals of Discrete Distributions (2014, background): “However, it is no longer minimax under other loss functions such as l1 loss, which was investigated in [47].”
Minimax estimation of discrete distributions (2015, background): “…in stochastic pro cesses: Marton and Shields [2] showed that, in a stationary ergodic stochastic process with sample size n and entropy rate H, the joint d-tuple distribution of the process can be consistently estimated using the empirical distribution if and only if d ::; ( 1-� In n for any E > O.”