9,951 research outputs found
-Divergence Inequalities via Functional Domination
This paper considers derivation of -divergence inequalities via the
approach of functional domination. Bounds on an -divergence based on one or
several other -divergences are introduced, dealing with pairs of probability
measures defined on arbitrary alphabets. In addition, a variety of bounds are
shown to hold under boundedness assumptions on the relative information. The
journal paper, which includes more approaches for the derivation of
f-divergence inequalities and proofs, is available on the arXiv at
https://arxiv.org/abs/1508.00335, and it has been published in the IEEE Trans.
on Information Theory, vol. 62, no. 11, pp. 5973-6006, November 2016.Comment: A conference paper, 5 pages. To be presented in the 2016 ICSEE
International Conference on the Science of Electrical Engineering, Nov.
16--18, Eilat, Israel. See https://arxiv.org/abs/1508.00335 for the full
paper version, published as a journal paper in the IEEE Trans. on Information
Theory, vol. 62, no. 11, pp. 5973-6006, November 201
Comparison of Channels: Criteria for Domination by a Symmetric Channel
This paper studies the basic question of whether a given channel can be
dominated (in the precise sense of being more noisy) by a -ary symmetric
channel. The concept of "less noisy" relation between channels originated in
network information theory (broadcast channels) and is defined in terms of
mutual information or Kullback-Leibler divergence. We provide an equivalent
characterization in terms of -divergence. Furthermore, we develop a
simple criterion for domination by a -ary symmetric channel in terms of the
minimum entry of the stochastic matrix defining the channel . The criterion
is strengthened for the special case of additive noise channels over finite
Abelian groups. Finally, it is shown that domination by a symmetric channel
implies (via comparison of Dirichlet forms) a logarithmic Sobolev inequality
for the original channel.Comment: 31 pages, 2 figures. Presented at 2017 IEEE International Symposium
on Information Theory (ISIT
Intertwining and commutation relations for birth-death processes
Given a birth-death process on with semigroup
and a discrete gradient depending on a positive weight , we
establish intertwining relations of the form
, where is the Feynman-Kac
semigroup with potential of another birth-death process. We provide
applications when is nonnegative and uniformly bounded from below,
including Lipschitz contraction and Wasserstein curvature, various functional
inequalities, and stochastic orderings. Our analysis is naturally connected to
the previous works of Caputo-Dai Pra-Posta and of Chen on birth-death
processes. The proofs are remarkably simple and rely on interpolation,
commutation, and convexity.Comment: Published in at http://dx.doi.org/10.3150/12-BEJ433 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
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