The DOI matches its Crossref record; 21 of the 21 references it cites were found in a registry or an index.
Kullback-Leibler divergence estimation of continuous distributions
Abstract
We present a method for estimating the KL divergence between continuous densities and we prove it converges almost surely. Divergence estimation is typically solved estimating the densities first. Our main result shows this intermediate step is unnecessary and that the divergence can be either estimated using the empirical cdf or k-nearest-neighbour density estimation, which does not converge to the true measure for finite k. The convergence proof is based on describing the statistics of our estimator using waiting-times distributions, as the exponential or Erlang. We illustrate the proposed estimators and show how they compare to existing methods based on density estimation, and we also outline how our divergence estimators can be used for solving the two-sample problem.
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Wu, Y. (1999) · Technometrics · doi:10.1080/00401706.1999.10485951 · Cited by 27,221
On Information and Sufficiency
Kullback, S., & Leibler, R. A. (1951) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177729694 · Cited by 20,193
Information theory, inference, and learning algorithms
(2004) · Choice Reviews Online · doi:10.5860/choice.41-5949 · Cited by 6,362
Information Theory, Inference, and Learning Algorithms
(2004) · Kybernetes · doi:10.1108/03684920410534506 · Cited by 4,937
Kraskov, A., Stögbauer, H., & Grassberger, P. (2004) · Physical Review E · doi:10.1103/physreve.69.066138 · Cited by 3,512
Probability and Random Processes
(2004) · Elsevier eBooks · doi:10.1016/b978-0-12-172651-5.x5000-3 · Cited by 2,535
A Kernel Method for the Two-Sample-Problem
Gretton, A., Borgwardt, K. M., Rasch, M., Schölkopf, B., & Smola, A. J. (2007) · Advances in Neural Information Processing Systems 19 · doi:10.7551/mitpress/7503.003.0069 · Cited by 2,167
Probability and Random Processes.
Grimmett, G. R., & Stirzaker, D. R. (2001) · doi:10.1093/oso/9780198572237.001.0001 · Cited by 1,850
Estimation of entropy and mutual information
Paninski, L. (2003) · Neural Computation · doi:10.1162/089976603321780272 · Cited by 1,442
A family of algorithms for approximate bayesian inference
Minka, T. P., & Picard, R. W. (2001) · DSpace@MIT (Massachusetts Institute of Technology) · Cited by 882
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Considerate approaches to constructing summary statistics for ABC model selection
Barnes, C. P., Filippi, S., Stumpf, M. P. H., & Thorne, T. (2012) · Statistics and Computing · doi:10.1007/s11222-012-9335-7 · Cited by 61
Effective Molecular Dynamics from Neural Network-Based Structure Prediction Models
Jussupow, A., & Kaila, V. R. I. (2023) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.2c01027 · Cited by 42
Metadata
- Authors
- Perez-Cruz, F.
- Venue
- 2008 IEEE International Symposium on Information Theory
- Publisher
- IEEE
- Published
- 2008-07
- Pages
- 1666-1670
- OpenAlex
- W2001150023
- Cited by
- 400
- References
- 21
- FWCI
- 8.08
- Type
- conference paper
- Language
- en
- Open access
- closed
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