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Generalizing Skew Jensen Divergences and Bregman Divergences With Comparative Convexity

Nock, Richard; Nielsen, Frank

Description

Comparative convexity is a generalization of ordinary convexity based on abstract means instead of arithmetic means. We introduce the generalized skew Jensen divergences and their corresponding Bregman divergences with respect to comparative convexity. To illustrate those novel families of divergences, we consider the convexity induced by quasi-arithmetic means, and report explicit formula for the corresponding Bregman divergences. In particular, we show that those new Bregman divergences are...[Show more]

dc.contributor.authorNock, Richard
dc.contributor.authorNielsen, Frank
dc.date.accessioned2020-12-20T20:56:49Z
dc.date.available2020-12-20T20:56:49Z
dc.identifier.issn1070-9908
dc.identifier.urihttp://hdl.handle.net/1885/218066
dc.description.abstractComparative convexity is a generalization of ordinary convexity based on abstract means instead of arithmetic means. We introduce the generalized skew Jensen divergences and their corresponding Bregman divergences with respect to comparative convexity. To illustrate those novel families of divergences, we consider the convexity induced by quasi-arithmetic means, and report explicit formula for the corresponding Bregman divergences. In particular, we show that those new Bregman divergences are equivalent to conformal ordinary Bregman divergences on monotone embeddings, and further state related results.
dc.format.mimetypeapplication/pdf
dc.language.isoen_AU
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE Inc)
dc.sourceIEEE Signal Processing Letters
dc.titleGeneralizing Skew Jensen Divergences and Bregman Divergences With Comparative Convexity
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume24
dc.date.issued2017
local.identifier.absfor080201 - Analysis of Algorithms and Complexity
local.identifier.ariespublicationa383154xPUB8398
local.type.statusPublished Version
local.contributor.affiliationNock, Richard, College of Engineering and Computer Science, ANU
local.contributor.affiliationNielsen, Frank, Ecole Polytechnique
local.bibliographicCitation.issue8
local.bibliographicCitation.startpage1123
local.bibliographicCitation.lastpage1127
local.identifier.doi10.1109/LSP.2017.2712195
dc.date.updated2020-11-23T10:35:07Z
local.identifier.scopusID2-s2.0-85028406148
local.identifier.thomsonID000404291100005
CollectionsANU Research Publications

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