A Concentration Result of Estimating Phi-Divergence using Data Dependent Partition
Abstract
Estimation of the $\phi$-divergence between two unknown probability distributions using empirical data is a fundamental problem in information theory and statistical learning. We consider a multi-variate generalization of the data dependent partitioning method for estimating divergence between the two unknown distributions. Under the assumption that the distribution satisfies a power law of decay, we provide a convergence rate result for this method on the number of samples and hyper-rectangles required to ensure the estimation error is bounded by a given level with a given probability.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2018
- DOI:
- 10.48550/arXiv.1801.00852
- arXiv:
- arXiv:1801.00852
- Bibcode:
- 2018arXiv180100852L
- Keywords:
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- Mathematics - Probability;
- Mathematics - Statistics Theory
- E-Print:
- 15 pages