Related papers: Generalized Common Informations: Measuring Commonn…
We propose a notion of common information that allows one to quantify and separate the information that is shared between two random variables from the information that is unique to each. Our notion of common information is defined by an…
Wyner's common information was originally defined for a pair of dependent discrete random variables. Its significance is largely reflected in, hence also confined to, several existing interpretations in various source coding problems. This…
Recently, two extensions of Wyner's common information\textemdash exact and R\'enyi common informations\textemdash were introduced respectively by Kumar, Li, and El Gamal (KLE), and the present authors. The class of common information…
This paper introduces the notion of exact common information, which is the minimum description length of the common randomness needed for the exact distributed generation of two correlated random variables $(X,Y)$. We introduce the quantity…
Common information (CI) is ubiquitous in information theory and related areas such as theoretical computer science and discrete probability. However, because there are multiple notions of CI, a unified understanding of the deep…
One of the main notions of information theory is the notion of mutual information in two messages (two random variables in Shannon information theory or two binary strings in algorithmic information theory). The mutual information in $x$…
In this paper we generalize the notion of common information of two dependent variables introduced by G\'acs & K\"orner. They defined common information as the largest entropy rate of a common random variable two parties observing one of…
This paper generalizes Wyner's definition of common information of a pair of random variables to that of $N$ random variables. We prove coding theorems that show the same operational meanings for the common information of two random…
An important notion of common information between two random variables is due to Wyner. In this paper, we derive a lower bound on Wyner's common information for continuous random variables. The new bound improves on the only other general…
We explore the duality between the simulation and extraction of secret correlations in light of a similar well-known operational duality between the two notions of common information due to Wyner, and G\'acs and K\"orner. For the inverse…
The two most prevalent notions of common information (CI) are due to Wyner and Gacs-Korner and both the notions can be stated as two different characteristic points in the lossless Gray-Wyner region. Although the information theoretic…
Two familiar notions of correlation are rediscovered as extreme operating points for simulating a discrete memoryless channel, in which a channel output is generated based only on a description of the channel input. Wyner's "common…
We give an information-theoretic interpretation of Canonical Correlation Analysis (CCA) via (relaxed) Wyner's common information. CCA permits to extract from two high-dimensional data sets low-dimensional descriptions (features) that…
Wyner's Common Information and a natural relaxation are studied in the special case of Gaussian random variables. The relaxation replaces conditional independence by a bound on the conditional mutual information. The main contribution is…
The introduction of the partial information decomposition generated a flurry of proposals for defining an intersection information that quantifies how much of "the same information" two or more random variables specify about a target random…
We take a closer look at the structure of bivariate dependency induced by a pair of predictor random variables $(X_1, X_2)$ trying to synergistically, redundantly or uniquely encode a target random variable $Y$. We evaluate a recently…
Multivariate mutual information provides a conceptual framework for characterizing higher-order interactions in complex systems. Two well-known measures of multivariate information---total correlation and dual total correlation---admit a…
We study secure source-coding with causal disclosure, under the Gaussian distribution. The optimality of Gaussian auxiliary random variables is shown in various scenarios. We explicitly characterize the tradeoff between the rates of…
We study a generalized version of Wyner's common information problem (also coined the distributed source simulation problem). The original common information problem consists in understanding the minimum rate of the common input to…
We introduce an innovative and mathematically rigorous definition for computing common information from multi-view data, drawing inspiration from G\'acs-K\"orner common information in information theory. Leveraging this definition, we…