Related papers: Some new insights into information decomposition i…
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 partial information decomposition (PID) aims to quantify the amount of redundant information that a set of sources provides about a target. Here, we show that this goal can be formulated as a type of information bottleneck (IB) problem,…
We consider a decision aggregation problem with two experts who each make a binary recommendation after observing a private signal about an unknown binary world state. An agent, who does not know the joint information structure between…
The common cause principle for two random variables $A$ and $B$ is examined in the case of causal insufficiency, when their common cause $C$ is known to exist, but only the joint probability of $A$ and $B$ is observed. As a result, $C$…
Spuriousness arises when there is an association between two or more variables in a dataset that are not causally related. In this work, we propose an explainability framework to preemptively disentangle the nature of such spurious…
The conventional approach to the general Partial Information Decomposition (PID) problem has been redundancy-based: specifying a measure of redundant information between collections of source variables induces a PID via Moebius-Inversion…
We discuss the use of multivariate Granger causality in presence of redundant variables: the application of the standard analysis, in this case, leads to under-estimation of causalities. Using the un-normalized version of the causality…
The entropy of a pair of random variables is commonly depicted using a Venn diagram. This representation is potentially misleading, however, since the multivariate mutual information can be negative. This paper presents new measures of…
Redundancy of experimental data is the basic statistic from which the complexity of a natural phenomenon and the proper number of experiments needed for its exploration can be estimated. The redundancy is expressed by the entropy of…
The partial information decomposition (PID) framework is concerned with decomposing the information that a set of random variables has with respect to a target variable into three types of components: redundant, synergistic, and unique.…
Systems of interest for theoretical or experimental work often exhibit high-order interactions, corresponding to statistical interdependencies in groups of variables that cannot be reduced to dependencies in subsets of them. While still…
O-information is an information-theoretic metric that captures the overall balance between redundant and synergistic information shared by groups of three or more variables. To complement the global assessment provided by this metric, here…
In this paper, we revisit the discrete lossy Gray-Wyner problem. In particular, we derive its optimal second-order coding rate region, its error exponent (reliability function) and its moderate deviations constant under mild conditions on…
We consider the formalism of information decomposition of target effects from multi-source interactions, i.e. the problem of defining redundant and synergistic components of the information that a set of source variables provides about a…
The Bayesian measure of sample information about the parameter, known as Lindley's measure, is widely used in various problems such as developing prior distributions, models for the likelihood functions and optimal designs. The predictive…
Secure multi-party computation is a central problem in modern cryptography. An important sub-class of this are problems of the following form: Alice and Bob desire to produce sample(s) of a pair of jointly distributed random variables. Each…
Determining the strength of non-linear statistical dependencies between two variables is a crucial matter in many research fields. The established measure for quantifying such relations is the mutual information. However, estimating mutual…
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 address the problem of efficiently and informatively quantifying how multiplets of variables carry information about the future of the dynamical system they belong to. In particular we want to identify groups of variables carrying…
Here, we leverage recent advances in information theory to develop a novel method to characterise the dominant character of the high-order dependencies of quantum systems. To this end, we introduce the Q-information: an…