Related papers: Conditional and unconditional information inequali…
We propose two novel extensions of the Wyner common information optimization problem. Each relaxes one fundamental constraints in Wyner's formulation. The \textit{Variational Wyner Common Information} relaxes the matching constraint to the…
We give by simple arguments sufficient conditions, so called Lyapunov conditions, for Talagrand's transportation information inequality and for the logarithmic Sobolev inequality. Those sufficient conditions work even in the case where the…
We develop a dynamic model of economic complexity that endogenously generates a transition between unconditional and conditional convergence. In this model, convergence turns conditional as the capability intensity of activities rises. We…
We discuss possible criteria that may qualify or disqualify power indices for applications. Instead of providing final answers we merely ask questions that are relevant from our point of view and summarize some material from the literature.
The Ingleton inequality is a classical linear information inequality that holds for representable matroids but fails to be universally valid for entropic vectors. Understanding the extent to which this inequality can be violated has been a…
In this paper we present simple example of propositional logic which has one modal operator and is based on intuitionistic core. This system is very weak in modal sense - e.g. rules of regularity or monotonicity do not hold. It has complete…
In this paper, I argue that counterfactual fairness does not constitute a necessary condition for an algorithm to be fair, and subsequently suggest how the constraint can be modified in order to remedy this shortcoming. To this end, I…
We prove some Hardy-type inequalities via an approach that involves constructing auxiliary sequences.
In 1998, Zhang and Yeung found the first unconditional non-Shannon-type information inequality. Recently, Dougherty, Freiling and Zeger gave six new unconditional non-Shannon-type information inequalities. This work generalizes their work…
We consider the problem of assessing whether, in an individual case, there is a causal relationship between an observed exposure and a response variable. When data are available on similar individuals we may be able to estimate prospective…
We define a proof system for exceptions which is close to the syntax for exceptions, in the sense that the exceptions do not appear explicitly in the type of any expression. This proof system is sound with respect to the intended…
We investigate the information distribution among different entities in the weak measurements protocol. Focusing on multilevel, decaying systems under continuous (no-click) monitoring, we derive exact, conservation-type information…
In this short paper we show that the inequality of arithmetic and geometric means is reduced to another interesting inequality, and a proof is provided.
Impossibility results show that important fairness measures (independence, separation, sufficiency) cannot be satisfied at the same time under reasonable assumptions. This paper explores whether we can satisfy and/or improve these fairness…
A framework for a quantum mechanical information theory is introduced that is based entirely on density operators, and gives rise to a unified description of classical correlation and quantum entanglement. Unlike in classical (Shannon)…
Comparisons are made for the amount of agreement of the composite likelihood information criteria and their full likelihood counterparts when making decisions among the fits of different models, and some properties of penalty term for…
We provide a wide-ranging study of the scenario where a subset of the relations in a relational vocabulary are visible to a user --- that is, their complete contents are known --- while the remaining relations are invisible. We also have a…
A powerful way to understand a complex query is by observing how it operates on data instances. However, specific database instances are not ideal for such observations: they often include large amounts of superfluous details that are not…
This short note revisit information metric, underlining that it is a pseudo metric on manifolds of observables (random variables), rather than as usual on probability laws. Geodesics are characterized in terms of their boundaries and…
Bell nonlocality is one of the most intriguing and counter-intuitive phenomena displayed by quantum systems. Interestingly, such stronger-than-classical quantum correlations are somehow constrained, and one important question to the…