9,951 research outputs found

    ff-Divergence Inequalities via Functional Domination

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    This paper considers derivation of ff-divergence inequalities via the approach of functional domination. Bounds on an ff-divergence based on one or several other ff-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

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    This paper studies the basic question of whether a given channel VV can be dominated (in the precise sense of being more noisy) by a qq-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 χ2\chi^2-divergence. Furthermore, we develop a simple criterion for domination by a qq-ary symmetric channel in terms of the minimum entry of the stochastic matrix defining the channel VV. 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

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    Given a birth-death process on N\mathbb {N} with semigroup (Pt)t≥0(P_t)_{t\geq0} and a discrete gradient ∂u{\partial}_u depending on a positive weight uu, we establish intertwining relations of the form ∂uPt=Qt ∂u{\partial}_uP_t=Q_t\,{\partial}_u, where (Qt)t≥0(Q_t)_{t\geq0} is the Feynman-Kac semigroup with potential VuV_u of another birth-death process. We provide applications when VuV_u 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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