Competitive Distribution Estimation: Why is Good-Turing Good

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Learning Discrete Distributions from Untrusted Batches (2017, background): “Beyond this worst-case setting, there has also been signiﬁcant work considering this learning problem with the goal of developing “instance optimal” algorithms that leverage whatever structure might be present in the given distribution (see e.g. [OS15, VV16]).”
Formal Limitations on the Measurement of Mutual Information (2018, background): “The problem of estimating distributions and entropies from sample types has been investigated by various authors (McAllester and Schapire, 2000; Orlitsky et al., 2003; Orlitsky and Suresh, 2015; Arora et al., 2018).”
Instance optimal learning of discrete distributions (2016, result): “As was recently shown by Orlitsky and Suresh [29], for the task of learning a distribution of known support with respect to KL divergence, such methods achieve “instance optimal” results analogous to our results for this diﬀerent distance/divergence function.”