Related papers: On some entropy functionals derived from R\'enyi i…
We discuss how the method of maximum entropy, MaxEnt, can be extended beyond its original scope, as a rule to assign a probability distribution, to a full-fledged method for inductive inference. The main concept is the (relative) entropy…
In this paper we establish functional Erd\H{o}s-Renyi laws for L\'evy processes, i.e. limit theorems for sets of functions on [0,1] associated to their increments. First, we determine precise conditions under which, in a general framework,…
Probability distributions having power-law tails are observed in a broad range of social, economic, and biological systems. We describe here a potentially useful common framework. We derive distribution functions $\{p_k\}$ for situations in…
We describe and develop a close relationship between two problems that have customarily been regarded as distinct: that of maximizing entropy, and that of minimizing worst-case expected loss. Using a formulation grounded in the equilibrium…
In this paper, we provide the R\'enyi entropy and complexity measure for a novel, flexible class of skew-gaussian distributions and their related families, as a characteristic form of the skew-gaussian Shannon entropy. We give closed…
A formulation of the density functional theory is constructed on the foundations of entropic inference. The theory is introduced as an application of maximum entropy for inhomogeneous fluids in thermal equilibrium. It is shown that entropic…
The conventional channel resolvability problem refers to the determination of the minimum rate required for an input process so that the output distribution approximates a target distribution in either the total variation distance or the…
A framework for deriving R\'enyi entropy-power inequalities (EPIs) is presented that uses linearization and an inequality of Dembo, Cover, and Thomas. Simple arguments are given to recover the previously known R\'enyi EPIs and derive new…
Following a recent proof of Shannon's entropy power inequality (EPI), a comprehensive framework for deriving various EPIs for the R\'enyi entropy is presented that uses transport arguments from normal densities and a change of variable by…
We prove the large deviation principle for several entropy and cross entropy estimators based on return times and waiting times on shift spaces over finite alphabets. We consider shift-invariant probability measures satisfying some…
In data-driven determination of Parton Distribution Functions (PDFs) in global QCD analyses, uncovering the true underlying distributions is complicated by a highly convoluted inverse problem. The determination of PDFs can be understood as…
In this paper a new operational definition of Renyi entropy and Renyi divergence is presented. Other operational definitions are mentioned.
We use complex contour integral techniques to study the entropy H and subentropy Q as functions of the elementary symmetric polynomials, revealing a series of striking properties. In particular for these variables, derivatives of -Q are…
We provide an upper bound on the maximal entropy rate at which the entropy of the expected density operator of a given ensemble of two states changes under nonlocal unitary evolution. A large class of entropy measures in considered, which…
We present a systematic study of the reconstruction of a non-negative function via maximum entropy approach utilizing the information contained in a finite number of moments of the function. For testing the efficacy of the approach, we…
This article is a continuation of my paper [arxiv: 1409.1015v2]. R\'enyi and Tsallis entropies are associated to positive linear operators and properties of some functions related to these entropies are investigated.
In this study an attempt has been made to propose a way to develop new distribution. For this purpose, we need only idea about distribution function. Some important statistical properties of the new distribution like moments, cumulants,…
The purpose of this note is to give the general solution of two functional equations connected to the Shannon entropy and also to the Tsallis entropy. As a result of this, we present the regular solution of these equations, as well.…
Information functionals allow to quantify the degree of randomness of a given probability distribution, either absolutely (through min/max entropy principles) or relative to a prescribed reference one. Our primary aim is to analyze the…
Understanding how network function constrains neural connectivity is a central challenge in neuroscience. An influential approach is to train neural networks with gradient descent on cognitive tasks and characterize the resulting…