Edgeworth Approximation of Multivariate Differential Entropy

By Marc M. Van Hulle. 2005

119 citations recorded by the source corpus.

Subfields: Statistical and Nonlinear Physics, Statistics and Probability, Signal Processing

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Statistical and Nonlinear Physics

In Statistics and Probability

In Signal Processing

Citations in the corpus

Mutual Information Neural Estimation (2018, background): “…vector machines, non-parametric kernel-density estimators; see, Fraser & Swinney, 1986; Darbellay & Vajda, 1999; Suzuki et al., 2008; Kwak & Choi, 2002; Moon et al., 1995; Kraskov et al., 2004), or rely on approximate gaussianity of data distribution (e.g., Edgeworth expansion, Van Hulle, 2005).”
Sufficient Dimension Reduction via Squared-Loss Mutual Information Estimation (2010, methodology): “As summarized in Table 1, MLMI affords model selection by cross-variation, while there is no systematic method to choose tuning parameters for HSIC, KDR, and NN. MLMI does not require speciﬁc structures on the underlying distributions, and EDGE requires that the distributions are near gaussian.”
Parametric Bayesian Estimation of Differential Entropy and Relative Entropy (2010, methodology): “In other recent work on differential entropy estimation, Van Hulle took a semiparametric approach to nonparametric differential entropy estimation for a continuous density by using a 5th-order Edgeworth expansion about the maximum likelihood multivariate normal given the data samples drawn from a no”
MINE: Mutual Information Neural Estimation (2018, background): “Van Hulle (2005) presents an estimator built around the Edgeworth series (Hall, 2013).”
Bootstrap rank‐ordered conditional mutual information (broCMI): A nonlinear input variable selection method for water resources modeling (2016, methodology): “This modification is made possible via Edgeworth approximations enabling the estimation of arbitrary continuous multivariate probability distribution functions [Van Hulle, 2005].”
Empirical estimation of entropy functionals with confidence (2010, background): “These include consistent estimators based on entropic graphs [19, 36], gap estimators [43], nearest neighbor distances [17, 26, 29, 45], kernel density plug-in estimators [1, 11, 3, 18, 4, 16], Edgeworth approximations [21], convex risk minimization [35] and orthogonal projections [25].”