Convergence properties of functional estimates for discrete distributions

By András Antos, Ioannis Kontoyiannis. 2001

251 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/473ad681ca6e407e114a4435ed9491f8fb1b3304

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In Artificial Intelligence

Citations in the corpus

Estimation of Entropy and Mutual Information (2003, background): “Theorem 1 (Consistency).”
Minimax Estimation of Functionals of Discrete Distributions (2014, background): “[73] I. Kontoyiannis, P. H. Algoet, Y. M. Suhov, and A. Wyner, “Nonparametric entropy estimation for stationary processes and random fields, with applications to English text,” Information Theory, IEEE Transactions on, vol. 44, no. 3, pp. 1319–1327, 1998.”
Minimax estimation of discrete distributions (2015, background): “An evident proof of this fact is the following result by Antos and Kon toyiannis [10] on entropy estimation over countably infinite alphabet sizes.”
A Bernstein-Von Mises Theorem for discrete probability distributions (2008, background): “The problem of estimating such functionals has been investigated by Antos and Kontoyiannis (2001) and Paninski (2004).”
Minimax Rates of Entropy Estimation on Large Alphabets via Best Polynomial Approximation (2014, background): “Fixed alphabet For ﬁxed distribution P and n → ∞ , Antos and Kontoyiannis showed that [AK01] the plug-in estimator is always consistent and the asymptotic variance of the plug-in estimator is obtained in [Bas59].”
Maximum Likelihood Estimation of Functionals of Discrete Distributions (2014, unknown): “[49] A. Antos and I. Kontoyiannis, “Convergence properties of functional estimates for discrete distributions,” Random Structures & Algorithms, vol. 19, no. 3-4, pp. 163–193, 2001.”
A Robust-Equitable Measure for Feature Ranking and Selection (2017, background): “Over all distributions, even discrete ones, no uniform rate of convergence is possible for MI (Antos and Kontoyiannis, 2001; Paninski, 2003).”
Causality detection based on information-theoretic approaches in time series analysis (2007, background): “Convergence properties of discrete plug-in estimates Convergence properties of discrete plug-in estimators were studied by Antos and Kontoyiannis [9] in a more general scope.”
Estimating Renyi Entropy of Discrete Distributions (2014, methodology): “Shannon entropy was first estimated via an empirical estimator, analyzed in, for instance, [2].”