Related papers: Generalized Information Inequalities via Submodula…
This paper develops a geometric diagnostic framework for classical inequality decomposability. Representing the simplest nontrivial setting of three-person income distributions as points on the two-dimensional income-share simplex, we…
In this paper, we propose a new discriminative model named \emph{nonextensive information theoretical machine (NITM)} based on nonextensive generalization of Shannon information theory. In NITM, weight parameters are treated as random…
Entropic uncertainty relations are interesting in their own rights as well as for a lot of applications. Keeping this in mind, we try to make the corresponding inequalities as tight as possible. The use of parametrized entropies also allows…
Pseudoentropy characterizations provide a quantitatively precise demonstration of the close relationship between computational hardness and computational randomness. We prove a unified pseudoentropy characterization that generalizes and…
We provide extensions of geometric inequalities about sections and projections of convex bodies to the setting of integrable log-concave functions. Namely, we consider suitable generalizations of the affine and dual affine quermassintegrals…
Bounds on information combining are a fundamental tool in coding theory, in particular when analyzing polar codes and belief propagation. They usually bound the evolution of random variables with respect to their Shannon entropy. In recent…
We introduce the notion of consistent error bound functions which provides a unifying framework for error bounds for multiple convex sets. This framework goes beyond the classical Lipschitzian and H\"olderian error bounds and includes…
A new general decomposition theory inspired from modular graph decomposition is presented. This helps unifying modular decomposition on different structures, including (but not restricted to) graphs. Moreover, even in the case of graphs,…
In 1997, Z.Zhang and R.W.Yeung found the first example of a conditional information inequality in four variables that is not "Shannon-type". This linear inequality for entropies is called conditional (or constraint) since it holds only…
Greedy algorithms are widely used for problems in machine learning such as feature selection and set function optimization. Unfortunately, for large datasets, the running time of even greedy algorithms can be quite high. This is because for…
This paper addresses the correspondence between linear inequalities of Shannon entropy and differential entropy for sums of independent group-valued random variables. We show that any balanced (with the sum of coefficients being zero)…
Recently, two extensions of Wyner's common information\textemdash exact and R\'enyi common informations\textemdash were introduced respectively by Kumar, Li, and El Gamal (KLE), and the present authors. The class of common information…
Information diagram and the I-measure are useful mnemonics where random variables are treated as sets, and entropy and mutual information are treated as a signed measure. Although the I-measure has been successful in machine proofs of…
In this note, we present two general classes of integral inequalities motivated by their applications to infinite dimensional systems. The inequalities possess general structures in terms of weight functions and lower quadratic bounds. Many…
We consider the problem of maximizing submodular functions; while this problem is known to be NP-hard, several numerically efficient local search techniques with approximation guarantees are available. In this paper, we propose a novel…
Accurately matching visual and textual data in cross-modal retrieval has been widely studied in the multimedia community. To address these challenges posited by the heterogeneity gap and the semantic gap, we propose integrating Shannon…
Learning an appropriate (dis)similarity function from the available data is a central problem in machine learning, since the success of many machine learning algorithms critically depends on the choice of a similarity function to compare…
We discuss linear programming techniques that help to deduce corollaries of non classic inequalities for Shannon's entropy. We focus on direct applications of the copy lemma. These applications involve implicitly some (known or unknown)…
In this paper, we establish some new Hadamard type inequalities for s-logarithmically convex functions in the second sense via fractional integrals by using Lemma 1 which has been proved by Sarikaya et al. in the paper [3].
The entropy of a graph is an information-theoretic quantity which expresses the complexity of a graph \cite{DM1,M}. After Shannon introduced the definition of entropy to information and communication, many generalizations of the entropy…