Density-free convergence properties of various estimators of entropy
Computational Statistics & Data Analysis - Special issue on statistical data analysis based on the L:0I1:0E norm and relate
Elements of information theory
Elements of information theory
Independent component analysis, a new concept?
Signal Processing - Special issue on higher order statistics
The covering number in learning theory
Journal of Complexity
Kernel Methods for Pattern Analysis
Kernel Methods for Pattern Analysis
Parametric estimation and tests through divergences and the duality technique
Journal of Multivariate Analysis
Some inequalities for information divergence and related measures of discrimination
IEEE Transactions on Information Theory
Divergence Estimation of Continuous Distributions Based on Data-Dependent Partitions
IEEE Transactions on Information Theory
On Divergences and Informations in Statistics and Information Theory
IEEE Transactions on Information Theory
Neural Networks
Neural Computation
Change-point detection with feature selection in high-dimensional time-series data
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Hi-index | 754.85 |
We develop and analyze M-estimation methods for divergence functionals and the likelihood ratios of two probability distributions. Our method is based on a nonasymptotic variational characterization of f-divergences, which allows the problem of estimating divergences to be tackled via convex empirical risk optimization. The resulting estimators are simple to implement, requiring only the solution of standard convex programs. We present an analysis of consistency and convergence for these estimators. Given conditions only on the ratios of densities, we show that our estimators can achieve optimal minimax rates for the likelihood ratio and the divergence functionals in certain regimes. We derive an efficient optimization algorithm for computing our estimates, and illustrate their convergence behavior and practical viability by simulations.