Related papers: Conditional and unconditional information inequali…
New concept of conditional differential invariant is discussed that would allow description of equations invariant with respect to an operator under a certain condition. Example of conditional invariants of the projective operator is…
We present a key example from sequential analysis, which illustrates that conditional bias reduction can cause infinite mean absolute error.
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…
In this work, we analyse how to define a conditional version of Sibson's $\alpha$-Mutual Information. Several such definitions can be advanced and they all lead to different information measures with different (but similar) operational…
This work proposes a complete algebraic model for classical information theory. As a precursor the essential probabilistic concepts have been defined and analyzed in the algebraic setting. Examples from probability and information theory…
The derivation of Bell inequalities in terms of quantum statistical (thermodynamic) entropies is considered. Inequalities of the Wigner form are derived but shown to be extremely limiting in their applicability due to the nature of the…
Using known entropic and information inequalities new inequalities for some classical polynomials are obtained. Examples of Jacobi and Legendre polynomials are considered.
In this note I give an information-theoretic proof of the Bonami-Beckner-Gross hypercontractive inequality.
We obtain simple proofs of certain inequalites for bivariate means.
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…
A concrete, stylized example illustrates that inferences may be degraded, rather than improved, by incorporating supplementary data via a joint likelihood. In the example, the likelihood is assumed to be correctly specified, as is the prior…
This note provides examples of all possible equality and strict inequality relations between upper and lower Abelian and Cesaro limits of sequences bounded above or below.
We prove a conditional decoupling inequality for the model of random interlacements in dimension $d\geq 3$: the conditional law of random interlacements on a box (or a ball) $A_1$ given the (not very "bad") configuration on a "distant" set…
We provide an overview of the connections between Bell's inequalities and algebraic structure.
We comment on one of the earliest derivations of the so-called wave-particle duality relation. Our aim is to point out a slight technical flaw in the proof, fixing it. Neither the physical content of the duality relation nor its validity is…
We show that moment inequalities in a wide variety of economic applications have a particular linear conditional structure. We use this structure to construct uniformly valid confidence sets that remain computationally tractable even in…
We define a notion of a weak canonical base for a partial type. This notion is weaker than the usual canonical base for an amalgamation base. We prove that certain family of partial types have a weak canonical base. This family clearly…
We identify conditional parity as a general notion of non-discrimination in machine learning. In fact, several recently proposed notions of non-discrimination, including a few counterfactual notions, are instances of conditional parity. We…
Causal parameters may not be point identified in the presence of unobserved confounding. However, information about non-identified parameters, in the form of bounds, may still be recovered from the observed data in some cases. We develop a…
Algebraic effects are computational effects that can be described with a set of basic operations and equations between them. As many interesting effect handlers do not respect these equations, most approaches assume a trivial theory,…