Total Correlation of Gaussian Vector Sources on the Gray–Wyner Network

Michael Christoph Gastpar
2016
Article de conférence

We study a generalization of Wyner’s Common Information to Watanabe’s Total Correlation. The first minimizes the description size required for a variable that can make two other random variables conditionally independent. If independence is unattainable, Watanabe’s total (conditional) correlation is measure to check just how independent they have become. Following up on earlier work for scalar Gaussians, we discuss the minimization of total correlation for Gaussian vector sources. Using Gaussian auxiliaries, we show one should transform two vectors of length d into d independent pairs, after which a reverse water filling procedure distributes the minimization over all these pairs. Lastly, we show how this minimization of total conditional correlation fits a lossy coding problem by using the Gray–Wyner network as a model for a caching problem.

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Michael Christoph Gastpar
2016
Article de conférence

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https://infoscience.epfl.ch/record/222848?ln=fr

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Concepts associés

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Caching Gaussians: Minimizing Total Correlation on the Gray–Wyner Network

Michael Christoph Gastpar

We study a caching problem that resembles a lossy Gray–Wyner network: A source produces vector samples from a Gaussian distribution, but the user is interested in the samples of only one component. The encoder first sends a cache message without any knowledge of the user’s preference. Upon learning her request, a second message is provided in the update phase so as to attain the desired fidelity on that component. The cache is efficient if it exploits as much of the correlation in the source as possible, which connects to the notions of Wyner’s common information (for high cache rates) and Watanabe’s total correlation (for low cache rates). For the former, we extend known results for 2 Gaussians to multivariates by showing that common information is a simple linear program, which can be solved analytically for circulant correlation matrices. Total correlation in a Gaussian setting is less well-studied. We show that for bivariates and using Gaussian auxiliaries it is captured in the dominant eigenvalue of the correlation matrix. For multivariates the problem is a more difficult optimization over a non-convex domain, but we conjecture that circulant matrices may again be analytically solvable.

Ieee2016

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Caching (Bivariate) Gaussians

Michael Christoph Gastpar, Guillaume Jean Op 't Veld

Caching is a technique that alleviates networks during peak hours by transmitting partial information before a request for any is made. In a lossy setting of Gaussian databases, we study a single-user model in which good caching strategies minimize the data still needed on average once the user requests a file. The encoder decides on a caching strategy by weighing the benefit from two key parameters: the prior preference for a file and the correlation among the files. Considering uniform prior preference but correlated files, caching becomes an application of Wyner's common information and Watanabe's total correlation. We show this case triggers a split: caching Gaussian sources is a non-convex optimization problem unless one spends enough rate to cache all the common information between files. Combining both correlation and user preference we explicitly characterize the full trade-off when the encoder uses Gaussian codebooks in a database of two files: we show that as the size of the cache increases, the encoder should change strategy and increasingly prioritize user preference over correlation. In this specific case we also address the loss in performance incurred if the encoder has no knowledge of the user's preference and show that this loss is bounded.

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

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Corrélation (statistiques)

En probabilités et en statistique, la corrélation entre plusieurs variables aléatoires ou statistiques est une notion de liaison qui contredit leur indépendance. Cette corrélation est très souvent

Common Information Model

CIM signifie « modèle de données unifié » (Common Information Model). C'est un standard ouvert qui définit comment des éléments administrés dans un environnement informatique peuvent être représentés

Cache de processeur

Un cache de processeur est une antémémoire matérielle utilisée par l'unité centrale de traitement (CPU) d'un ordinateur pour réduire le coût moyen (temps ou énergie) de l’accès aux données de la mémo