Related papers: On Phi-entropic Dependence Measures and Non-local …
This paper proposes that common measures for network transitivity, based on the enumeration of transitive triples, do not reflect the theoretical statements about transitivity they aim to describe. These statements are often formulated as…
The question of how quantities, like entanglement and coherence, depend on the number of copies of a given state $\rho$ is addressed. This is a hard problem, often involving optimizations over Hilbert spaces of large dimensions. Here, we…
Dependence among marginally constrained observations can break a finite-sample barrier. To formalize this phenomenon, we introduce the \emph{minimum list entropy coupling} $H(P\|Q_1,\dots,Q_m)$, the minimum conditional entropy…
Characterising the capacity region for a network can be extremely difficult. Even with independent sources, determining the capacity region can be as hard as the open problem of characterising all information inequalities. The majority of…
In this paper we propose and study a class of simple, nonparametric, yet interpretable measures of association between two random variables $X$ and $Y$ taking values in general topological spaces. These nonparametric measures -- defined…
We establish a precise connection between statistical significance in dependence testing and information-theoretic dependence as quantified by Shannon mutual information (MI). In the absence of prior distributional information, we consider…
We devised a measure based on the distributions of relative event timings of two coupled units. The measure dynamically evaluates temporal interdependencies between the two coupled units. Using this we show that even in the event of…
Entropy is a measure of self-information which is used to quantify losses. Entropy was developed in thermodynamics, but is also used to compare probabilities based on their deviating information content. Corresponding model uncertainty is…
Measuring dependence between random variables is a fundamental problem in Statistics, with applications across diverse fields. While classical measures such as Pearson's correlation have been widely used for over a century, they have…
Empirical process theory for i.i.d. observations has emerged as a ubiquitous tool for understanding the generalization properties of various statistical problems. However, in many applications where the data exhibit temporal dependencies…
It is well known that the entropy $H(X)$ of a discrete random variable $X$ is always greater than or equal to the entropy $H(f(X))$ of a function $f$ of $X$, with equality if and only if $f$ is one-to-one. In this paper, we give tight…
How does the information flow between different brain regions during various stimuli? This is the question we aim to address by studying complex cognitive paradigms in terms of Information Theory. To assess creativity and the emergence of…
Information theory provides ideas for conceptualising information and measuring relationships between objects. It has found wide application in the sciences, but economics and finance have made surprisingly little use of it. We show that…
In this paper, the maximal nonlinear conditional correlation of two random vectors $X$ and $Y$ given another random vector $Z$, denoted by $\rho_1(X,Y|Z)$, is defined as a measure of conditional association, which satisfies certain…
Based on recent progress in research on copula based dependence measures, we review the original Renyi's axioms on symmetric measures and propose a new set of axioms that applies to nonsymmetric measures. We show that nonsymmetric measures…
We introduce a novel measure of dependence that captures the extent to which a random variable $Y$ is determined by a random vector $X$. The measure equals zero precisely when $Y$ and $X$ are independent, and it attains one exactly when $Y$…
It is well known that estimating the expectation of any given bounded random variable with values in $[-B, B]$ has a sample complexity of $\mathrm{O}(B^2/\epsilon^2)$ that is independent of the underlying probability measure. We show that…
A fundamental task in statistical learning is quantifying the joint dependence or association between two continuous random variables. We introduce a novel, fully non-parametric measure that assesses the degree of association between…
The strength of quantum correlations is bounded from above by Tsirelson's bound. We establish a connection between this bound and the fact that correlations between two systems cannot increase under local operations, a property known as the…
We propose a novel approach to concentration for non-independent random variables. The main idea is to ``pretend'' that the random variables are independent and pay a multiplicative price measuring how far they are from actually being…