Generalised pinsker inequalities

Mark D. Reid; Robert C. Williamson

Generalised pinsker inequalities

Mark D. Reid, Robert C. Williamson

Research output: Contribution to conference › Paper › peer-review

15 Citations (Scopus)

Abstract

We generalise the classical Pinsker inequality which relates variational divergence to Kullback-Liebler divergence in two ways: we consider arbitrary f-divergences in place of KL divergence, and we assume knowledge of a sequence of values of generalised variational divergences. We then develop a best possible inequality for this doubly generalised situation. Specialising our result to the classical case provides a new and tight explicit bound relating KL to variational divergence (solving a problem posed by Vajda some 40 years ago). The solution relies on exploiting a connection between divergences and the Bayes risk of a learning problem via an integral representation.

Original language	English
Publication status	Published - 2009
Event	22nd Conference on Learning Theory, COLT 2009 - Montreal, QC, Canada Duration: 18 Jun 2009 → 21 Jun 2009

Conference

Conference	22nd Conference on Learning Theory, COLT 2009
Country/Territory	Canada
City	Montreal, QC
Period	18/06/09 → 21/06/09

Cite this

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title = "Generalised pinsker inequalities",

abstract = "We generalise the classical Pinsker inequality which relates variational divergence to Kullback-Liebler divergence in two ways: we consider arbitrary f-divergences in place of KL divergence, and we assume knowledge of a sequence of values of generalised variational divergences. We then develop a best possible inequality for this doubly generalised situation. Specialising our result to the classical case provides a new and tight explicit bound relating KL to variational divergence (solving a problem posed by Vajda some 40 years ago). The solution relies on exploiting a connection between divergences and the Bayes risk of a learning problem via an integral representation.",

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AU - Reid, Mark D.

AU - Williamson, Robert C.

PY - 2009

Y1 - 2009

N2 - We generalise the classical Pinsker inequality which relates variational divergence to Kullback-Liebler divergence in two ways: we consider arbitrary f-divergences in place of KL divergence, and we assume knowledge of a sequence of values of generalised variational divergences. We then develop a best possible inequality for this doubly generalised situation. Specialising our result to the classical case provides a new and tight explicit bound relating KL to variational divergence (solving a problem posed by Vajda some 40 years ago). The solution relies on exploiting a connection between divergences and the Bayes risk of a learning problem via an integral representation.

AB - We generalise the classical Pinsker inequality which relates variational divergence to Kullback-Liebler divergence in two ways: we consider arbitrary f-divergences in place of KL divergence, and we assume knowledge of a sequence of values of generalised variational divergences. We then develop a best possible inequality for this doubly generalised situation. Specialising our result to the classical case provides a new and tight explicit bound relating KL to variational divergence (solving a problem posed by Vajda some 40 years ago). The solution relies on exploiting a connection between divergences and the Bayes risk of a learning problem via an integral representation.

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M3 - Paper

AN - SCOPUS:84898062350

T2 - 22nd Conference on Learning Theory, COLT 2009

Y2 - 18 June 2009 through 21 June 2009

ER -

Generalised pinsker inequalities

Abstract

Conference

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