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We demonstrate that a popular class of nonparametric mutual information (MI) estimators based on k-nearest-neighbor graphs requires number of samples that scales exponentially with the true MI.
The proof and measurement of association between two things
C. Spearman · 1904
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Satosi Watanabe · 1960
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Probability theory of classical Euclidean optimization problems
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T.M. Cover and J.A. Thomas · 2006
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Relative performance of mutual information estimation methods for quantifying the dependence among short and noisy data
Shiraj Khan, Sharba Bandyopadhyay, Auroop R. Ganguly, Sunil Saigal, David J. Erickson, Vladimir Protopopescu, and George Ostrouchov · 2007
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Gábor J Székely, Maria L Rizzo, et al · 2009
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Estimation of mutual information: A survey
Janett Walters-Williams and Yan Li · 2009
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Divergence estimation for multidimensional densities via k-nearest-neighbor distances
Q. Wang, S.R. Kulkarni, and S. Verdú · 2009
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Elia Liitiäinen, Amaury Lendasse, and Francesco Corona · 2010
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Andreas Müller, Sebastian Nowozin, and Christoph Lampert · 2012
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Estimation of nonlinear functionals of densities with confidence
K. Sricharan, R. Raich, and A.O. Hero · 2012
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A consistent multivariate test of association based on ranks of distances
Ruth Heller, Yair Heller, and Malka Gorfine · 2013
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Ensemble estimators for multivariate entropy estimation
K. Sricharan, D. Wei, and A.O. Hero · 2013
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Density estimation from unweighted k-nearest neighbor graphs: a roadmap
Ulrike Von Luxburg and Morteza Alamgir · 2013
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Equitability, mutual information, and the maximal information coefficient
J. Kinney and G. Atwal · 2014
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