Back to Search
Start Over
Nearest Neighbor Density Functional Estimation From Inverse Laplace Transform.
- Source :
- IEEE Transactions on Information Theory; Jun2022, Vol. 68 Issue 6, p3511-3551, 41p
- Publication Year :
- 2022
-
Abstract
- A new approach to $L_{2}$ -consistent estimation of a general density functional using $k$ -nearest neighbor distances is proposed, where the functional under consideration is in the form of the expectation of some function $f$ of the densities at each point. The estimator is designed to be asymptotically unbiased, using the convergence of the normalized volume of a $k$ -nearest neighbor ball to a Gamma distribution in the large-sample limit, and naturally involves the inverse Laplace transform of a scaled version of the function $f$. Some instantiations of the proposed estimator recover existing $k$ -nearest neighbor based estimators of Shannon and Rényi entropies and Kullback–Leibler and Rényi divergences, and discover new consistent estimators for many other functionals such as logarithmic entropies and divergences. The $L_{2}$ -consistency of the proposed estimator is established for a broad class of densities for general functionals, and the convergence rate in mean squared error is established as a function of the sample size for smooth, bounded densities. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 68
- Issue :
- 6
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 157007230
- Full Text :
- https://doi.org/10.1109/TIT.2022.3151231