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Publication

Lower-bounds on the Bayesian Risk in Estimation Procedures via f–Divergences

Michael Christoph Gastpar, Amedeo Roberto Esposito, Adrien Vandenbroucque
2022
Conference Papers

Abstract

We consider the problem of parameter estimation in a Bayesian setting and propose a general lower-bound that includes part of the family of f-Divergences. The results are then applied to specific settings of interest and compared to other notable results in the literature. In particular, we show that the known bounds using Mutual Information can be improved by using, for example, Maximal Leakage, Hellinger divergence, or generalizations of the Hockey-Stick divergence.

Official source

https://infoscience.epfl.ch/entities/publication/cdc291a0-eb4e-4950-91b1-2bc5914cb6a9

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Michael Christoph Gastpar, Amedeo Roberto Esposito, Adrien Vandenbroucque
2022
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/cdc291a0-eb4e-4950-91b1-2bc5914cb6a9

About this result

Related concepts (28)

F-divergence

In probability theory, an -divergence is a function that measures the difference between two probability distributions and . Many common divergences, such as KL-divergence, Hellinger distance, and total variation distance, are special cases of -divergence. These divergences were introduced by Alfréd Rényi in the same paper where he introduced the well-known Rényi entropy. He proved that these divergences decrease in Markov processes.

Divergence (statistics)

In information geometry, a divergence is a kind of statistical distance: a binary function which establishes the separation from one probability distribution to another on a statistical manifold. The simplest divergence is squared Euclidean distance (SED), and divergences can be viewed as generalizations of SED. The other most important divergence is relative entropy (also called Kullback–Leibler divergence), which is central to information theory.

Kullback–Leibler divergence

In mathematical statistics, the Kullback–Leibler divergence (also called relative entropy and I-divergence), denoted , is a type of statistical distance: a measure of how one probability distribution P is different from a second, reference probability distribution Q. A simple interpretation of the KL divergence of P from Q is the expected excess surprise from using Q as a model when the actual distribution is P.

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