Nonparametric entropy estimation. An overview

By Jan Beirlant, E. Dudewicz, László Györfi, I. Denes. 1997

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Citations in the corpus

Consistency of Causal Inference under the Additive Noise Model (2013, methodology): “Note that, under our conditions on σ both H (pn,̄Y ) and H (pn,̄X ) are respectively consistent estimators of H (ηY,f ) , H(η) and H (ηX,g) (see e.g. (Beirlant et al., 1997)).”
Computational Optimal Transport (2018, background): “32) see Beirlant et al. [1997] for a review of non-parametric entropy estimators.”
Estimation of Entropy and Mutual Information (2003, background): “istence or smoothness of a density for P(X, Y). To our knowledge, results of this generality are unavailable outside the discrete context (but see Beirlant, Dudewicz, Gyorfi, & van der Meulen, 1997 ) for a good review of differential entropy estimation techniques, which provide a powerful alternati”
minet: A R/Bioconductor Package for Inferring Large Transcriptional Networks Using Mutual Information (2008, background): “Other interesting approaches can be found in [ 22-26 ].”
Benchmarking for Steganography (2008, background): “A good review of entropy estimators is in [3].”
ICA Using Spacings Estimates of Entropy (2003, background): “this estimator also becomes consistent ([1]).”
A new class of random vector entropy estimators and its applications in testing statistical hypotheses (2005, background): “They discussed a class of statistics based on the kernel-type estimators of density [23].”
Non-linear Causal Inference using Gaussianity Measures (2014, background): “In particular, the entropy is a quantity that is particularly difficult to estimate in practice (Beirlant et al., 1997).”
Directional multiscale modeling of images using the contourlet transform (2006, methodology): “We resort to nonparametric histogram estimation of mutual information [25], [26] between contourlet coefficients and their generalized neighborhoods.”
Information-theoretic analysis of interscale and intrascale dependencies between image wavelet coefficients (2001, background): “This problem is at least as difficult as pdf estimation; see [42], [ 43 ] for estimation of entropy in a general, theoretical context.”
Fast Multidimensional Entropy Estimation by $k$-d Partitioning (2009, background): “While estimators can be constructed based on an assumed parametric form for , nonparametric estimators [4] can avoid errors due to model misspecification [5].”
Efficient multivariate entropy estimation via $k$-nearest neighbour distances (2016, methodology): “See, for example, Beirlant et al. (1997) and Paninski (2003) for other applications and an overview of nonparametric techniques, which include methods based on sample spacings in the univariate case (e.”
Information theoretical estimators toolbox (2014, background): “The ITE package is self-contained, it only needs a Matlab or an Octave environment4 with standard toolboxes.”
Design of computer experiments: space filling and beyond (2011, unknown): “samples, and one may refer for instance to the survey papers (Hall and Morton 1993; Beirlant et al. 1997) for an overview.”
Estimation of Renyi information divergence via pruned minimal spanning trees (1999, background): “For an overview of entropy and I-divergence estimation applications the reader can refer to [2] and [1].”
Guessing human-chosen secrets (2012, background): “provide a good survey of estimation approaches [30].”