Efficient multivariate entropy estimation via \(k\)-nearest neighbour distances

DOI10.1214/18-AOS1688zbMath1473.62177arXiv1606.00304MaRDI QIDQ1731757

Ming Yuan, Richard J. Samworth, Thomas B. Berrett

Publication date: 14 March 2019

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.00304

zbMATH Keywords

Kozachenko-Leonenko estimator

Mathematics Subject Classification ID

Estimation in multivariate analysis (62H12) Nonparametric estimation (62G05) Statistical aspects of information-theoretic topics (62B10)

Related Items

Entropy-based test for generalised Gaussian distributions, A test for independence via Bayesian nonparametric estimation of mutual information, Ultra-High Dimensional Variable Selection for Doubly Robust Causal Inference, Dimensional measures of generalized entropy, Unnamed Item, Entropy estimation via uniformization, Local nearest neighbour classification with applications to semi-supervised learning, Optimal Nonparametric Inference with Two-Scale Distributional Nearest Neighbors, Efficient functional estimation and the super-oracle phenomenon, On Azadkia-Chatterjee's conditional dependence coefficient, The Hellinger Correlation, Variance Reduction for Estimation of Shapley Effects and Adaptation to Unknown Input Distribution, Efficient multivariate entropy estimation via \(k\)-nearest neighbour distances, Exact upper bound on the sum of squared nearest-neighbor distances between points in a rectangle, A Bayesian nonparametric estimation to entropy, Statistical estimation of mutual information for mixed model, On the estimation of entropy for non-negative data, On the Kozachenko-Leonenko entropy estimator, Large-scale multiple inference of collective dependence with applications to protein function, Optimal rates of entropy estimation over Lipschitz balls, A nearest-neighbor based nonparametric test for viral remodeling in heterogeneous single-cell proteomic data, Semiparametric density testing in the contamination model, A density based empirical likelihood approach for testing bivariate normality, Statistical estimation of conditional Shannon entropy, Theoretical analysis of cross-validation for estimating the risk of the k-Nearest Neighbor classifier, The entropy based goodness of fit tests for generalized von Mises-Fisher distributions and beyond

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the Kozachenko-Leonenko entropy estimator
• Testing composite hypotheses, Hermite polynomials and optimal estimation of a nonsmooth functional
• \(k_n\)-nearest neighbor estimators of entropy
• Lectures on the nearest neighbor method
• Sample estimate of the entropy of a random vector
• On the estimation of entropy
• On estimation of the \(L_r\) norm of a regression function
• Efficient multivariate entropy estimation via \(k\)-nearest neighbour distances
• Efficient estimation of integral functionals of a density
• On entropy estimation by \(m\)-spacing method
• Empirical Processes with Applications to Statistics
• Undersmoothed Kernel Entropy Estimators
• On the logarithms of high-order spacings
• Asymptotic Statistics
• 10.1162/jmlr.2003.4.7-8.1271
• A new class of random vector entropy estimators and its applications in testing statistical hypotheses
• An Introduction to Stein's Method
• Demystifying Fixed <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math> </inline-formula>-Nearest Neighbor Information Estimators
• Estimation of Entropy and Mutual Information
• Ensemble Estimators for Multivariate Entropy Estimation