On the Jensen-Shannon divergence and the variation distance for categorical probability distributions

Title:

On the Jensen-Shannon divergence and the variation distance for categorical probability distributions

Creator:

Corander, Jukka, Remes, Ulpu, and Koski, Timo

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:6144deec-9756-4cd9-a054-962e191a66c9
uuid:6144deec-9756-4cd9-a054-962e191a66c9
doi:10.14736/kyb-2021-6-0879

Subject:

blended divergences, Chan-Darwiche metric, likelihood-free inference, implicit maximum likelihood, reverse Pinsker inequality, and simulator-based inference

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We establish a decomposition of the Jensen-Shannon divergence into a linear combination of a scaled Jeffreys' divergence and a reversed Jensen-Shannon divergence. Upper and lower bounds for the Jensen-Shannon divergence are then found in terms of the squared (total) variation distance. The derivations rely upon the Pinsker inequality and the reverse Pinsker inequality. We use these bounds to prove the asymptotic equivalence of the maximum likelihood estimate and minimum Jensen-Shannon divergence estimate as well as the asymptotic consistency of the minimum Jensen-Shannon divergence estimate. These are key properties for likelihood-free simulator-based inference.

Language:

English

Rights:

http://creativecommons.org/licenses/by-nc-sa/4.0/
policy:public

Coverage:

879-907

Source:

Kybernetika | 2021 Volume:57 | Number:6

Harvested from:

CDK

Metadata only:

false