Introduces retention profiles r(x) and localization ratio L(P) for row-wise KL contraction analysis in finite Markov chains, with convexity-gap identity equating divergence gap to mutual information and constructions decoupling L(P) from spectral gap and mixing time.
On Maximal Correlation, Hypercontractivity, and the Data Processing Inequality studied by Erkip and Cover
5 Pith papers cite this work. Polarity classification is still indexing.
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abstract
In this paper we provide a new geometric characterization of the Hirschfeld-Gebelein-R\'{e}nyi maximal correlation of a pair of random $(X,Y)$, as well as of the chordal slope of the nontrivial boundary of the hypercontractivity ribbon of $(X,Y)$ at infinity. The new characterizations lead to simple proofs for some of the known facts about these quantities. We also provide a counterexample to a data processing inequality claimed by Erkip and Cover, and find the correct tight constant for this kind of inequality.
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UNVERDICTED 5representative citing papers
Develops tractable node-differentially private algorithms for community estimation in fixed-community stochastic block models together with lower bounds on the privacy parameter ε needed for consistency.
InfoAtlas is a pretrained neural model for zero-shot mutual information estimation that matches state-of-the-art accuracy with 100x speedup and handles varying dimensions via a single model.
The work derives an approximate local secrecy capacity and defines secret local contraction coefficients as largest generalized eigenvalues of channel matrix pencils, obtained via local Euclidean geometry approximations to the wiretap channel optimization problem.
Survival probability maps for any nontrivial pair of unitaries cannot achieve point-wise complementary correlation over the full projective state space, imposing a unitary-geometric limit on anti-contrast.
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Retention Profiles and KL Contraction Bounds in Finite Markov Chains
Introduces retention profiles r(x) and localization ratio L(P) for row-wise KL contraction analysis in finite Markov chains, with convexity-gap identity equating divergence gap to mutual information and constructions decoupling L(P) from spectral gap and mixing time.
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Node-private community estimation in stochastic block models: Tractable algorithms and lower bounds
Develops tractable node-differentially private algorithms for community estimation in fixed-community stochastic block models together with lower bounds on the privacy parameter ε needed for consistency.
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InfoAtlas: A Foundation Model for Zero-Shot Statistical Dependence Estimate
InfoAtlas is a pretrained neural model for zero-shot mutual information estimation that matches state-of-the-art accuracy with 100x speedup and handles varying dimensions via a single model.
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Local Information-Theoretic Security via Euclidean Geometry
The work derives an approximate local secrecy capacity and defines secret local contraction coefficients as largest generalized eigenvalues of channel matrix pencils, obtained via local Euclidean geometry approximations to the wiretap channel optimization problem.
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Fundamental limits to contrast reversal of survival probability correlations
Survival probability maps for any nontrivial pair of unitaries cannot achieve point-wise complementary correlation over the full projective state space, imposing a unitary-geometric limit on anti-contrast.