Related papers: On conditional Sibson's $\alpha$-Mutual Informatio…
A conditional version of Sibson's $\alpha$-information is defined using a simple closed-form "log-expectation" expression, which satisfies important properties such as consistency, uniform expansion, and data processing inequalities. This…
We explore a family of information measures that stems from R\'enyi's $\alpha$-Divergences with $\alpha<0$. In particular, we extend the definition of Sibson's $\alpha$-Mutual Information to negative values of $\alpha$ and show several…
Information measures can be constructed from R\'enyi divergences much like mutual information from Kullback-Leibler divergence. One such information measure is known as Sibson $\alpha$-mutual information and has received renewed attention…
The current definition of a conditional probability distribution enables one to update probabilities only on the basis of stochastic information. This paper provides a definition for conditional probability distributions with non-stochastic…
The Pearson correlation, correlation ratio, and maximal correlation have been well-studied in the literature. In this paper, we study the conditional versions of these quantities. We extend the most important properties of the unconditional…
A simpler approach to the characterization of vanishing conditional mutual information is presented. Some remarks are given as well. More specifically, relating the conditional mutual information to a commutator is a very promising approach…
In this paper we investigate the notion of conditional independence and prove several information inequalities for conditionally independent random variables.
The aim of this work is to provide bounds connecting two probability measures of the same event using R\'enyi $\alpha$-Divergences and Sibson's $\alpha$-Mutual Information, a generalization of respectively the Kullback-Leibler Divergence…
We develop a general operational framework that formalizes the concept of conditional uncertainty in a measure-independent fashion. Our formalism is built upon a mathematical relation which we call conditional majorization. We define…
This paper presents a unified interpretation of $\alpha$-mutual information ($\alpha$-MI) in terms of generalized $g$-leakage. Specifically, we present a novel interpretation of $\alpha$-MI within an extended framework for quantitative…
When evaluating causal influence from one time series to another in a multivariate dataset it is necessary to take into account the conditioning effect of the other variables. In the presence of many variables, and possibly of a reduced…
Conditionals are useful for modelling, but are not always sufficiently expressive for capturing information accurately. In this paper we make the case for a form of conditional that is situation-based. These conditionals are more expressive…
We characterize the growth of the Sibson and Arimoto mutual informations and $\alpha$-maximal leakage, of any order that is at least unity, between a random variable and a growing set of noisy, conditionally independent and…
The conditional mutual information I(X;Y|Z) measures the average information that X and Y contain about each other given Z. This is an important primitive in many learning problems including conditional independence testing, graphical model…
We investigate the sample complexity of mutual information and conditional mutual information testing. For conditional mutual information testing, given access to independent samples of a triple of random variables $(A, B, C)$ with unknown…
This paper presents a logical approach to nonmonotonic reasoning based on the notion of a nonmonotonic consequence relation. A conditional knowledge base, consisting of a set of conditional assertions of the type "if ... then ...",…
$H$-mutual information ($H$-MI) is a wide class of information leakage measures, where $H=(\eta, F)$ is a pair of monotonically increasing function $\eta$ and a concave function $F$, which is a generalization of Shannon entropy. $H$-MI is…
In this paper we propose a many-valued temporal conditional logic. We start from a many-valued logic with typicality, and extend it with the temporal operators of the Linear Time Temporal Logic (LTL), thus providing a formalism which is…
Several recent works in communication systems have proposed to leverage the power of neural networks in the design of encoders and decoders. In this approach, these blocks can be tailored to maximize the transmission rate based on…
Estimation of information theoretic quantities such as mutual information and its conditional variant has drawn interest in recent times owing to their multifaceted applications. Newly proposed neural estimators for these quantities have…