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The R\'enyi entropy is a generalization of the Shannon entropy and is widely used in mathematical statistics and applied sciences for quantifying the uncertainty in a probability distribution. We consider estimation of the quadratic R\'enyi…

Statistics Theory · Mathematics 2013-03-08 David Källberg , Nikolaj Leonenko , Oleg Seleznjev

This paper presents a novel theoretical study of the general problem of multiple source adaptation using the notion of Renyi divergence. Our results build on our previous work [12], but significantly broaden the scope of that work in…

Machine Learning · Computer Science 2012-05-14 Yishay Mansour , Mehryar Mohri , Afshin Rostamizadeh

We find the value of constants related to constraints in characterization of some known statistical distributions and then we proceed to use the idea behind maximum entropy principle to derive generalized version of this distributions using…

Statistical Mechanics · Physics 2007-05-23 Oscar Sotolongo-Costa , Alejandro Gonzalez Gonzalez , Francois Brouers

We explore asymptotically optimal bounds for deviations of distributions of independent Bernoulli random variables from the Poisson limit in terms of the Shannon relative entropy and R\'enyi/Tsallis relative distances (including Pearson's…

Probability · Mathematics 2019-08-15 S. G. Bobkov , G. P. Chistyakov , F. Götze

Entropy and relative or cross entropy measures are two very fundamental concepts in information theory and are also widely used for statistical inference across disciplines. The related optimization problems, in particular the maximization…

Statistics Theory · Mathematics 2021-06-18 Abhik Ghosh , Ayanendranath Basu

The Renyi entropy with a free Renyi parameter $q$ is the most justified form of information entropy, and the Tsallis entropy may be regarded as a linear approximation to the Renyi entropy when $q\simeq 1$. When $q\to 1$, both entropies go…

Statistical Mechanics · Physics 2007-05-23 Andrei G. Bashkirov

Entropy Estimation is an important problem with many applications in cryptography, statistic,machine learning. Although the estimators optimal with respect to the sample complexity have beenrecently developed, there are still some…

Data Structures and Algorithms · Computer Science 2020-02-24 Maciej Skorski

The Renyi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies or…

Quantum Physics · Physics 2014-01-28 Martin Müller-Lennert , Frédéric Dupuis , Oleg Szehr , Serge Fehr , Marco Tomamichel

Given a sample of independent and identically distributed random variables, a novel nonparametric maximum entropy method is presented to estimate the underlying continuous univariate probability density function (pdf). Estimates are found…

Probability · Mathematics 2016-06-30 Jenny Farmer , Donald J. Jacobs

The Matrix-based Renyi's entropy enables us to directly measure information quantities from given data without the costly probability density estimation of underlying distributions, thus has been widely adopted in numerous statistical…

Machine Learning · Statistics 2022-05-17 Yuxin Dong , Tieliang Gong , Shujian Yu , Chen Li

Entropy is a measure of self-information which is used to quantify losses. Entropy was developed in thermodynamics, but is also used to compare probabilities based on their deviating information content. Corresponding model uncertainty is…

Probability · Mathematics 2018-01-23 Alois Pichler , Ruben Schlotter

We consider the maximum entropy problems associated with R\'enyi $Q$-entropy, subject to two kinds of constraints on expected values. The constraints considered are a constraint on the standard expectation, and a constraint on the…

Information Theory · Computer Science 2008-12-18 Jean-François Bercher

In this paper, we obtain a new characterization result for symmetric distributions based on the entropy measure. Using the characterization, we propose a nonparametric test to test the symmetry of a distribution. We also develop the…

Statistics Theory · Mathematics 2025-05-14 Ganesh Vishnu Avhad , Ananya Lahiri , Sudheesh K. Kattumannil

We introduce some new classes of unimodal rotational invariant directional distributions, which generalize von Mises-Fisher distribution. We propose three types of distributions, one of which represents axial data. For each new type we…

Statistics Theory · Mathematics 2020-10-22 Nikolai Leonenko , Vitalii Makogin , Mehmet Siddik Cadirci

Entropy is the measure of uncertainty in any data and is adopted for maximisation of mutual information in many remote sensing operations. The availability of wide entropy variations motivated us for an investigation over the suitability…

Computer Vision and Pattern Recognition · Computer Science 2014-05-25 Dr. S. K. Katiyar , Arun P. V.

We present novel bounds for estimating discrete probability distributions under the $\ell_\infty$ norm. These are nearly optimal in various precise senses, including a kind of instance-optimality. Our data-dependent convergence guarantees…

Statistics Theory · Mathematics 2024-02-14 Aryeh Kontorovich , Amichai Painsky

Semi-continuous data comes from a distribution that is a mixture of the point mass at zero and a continuous distribution with support on the positive real line. A clear example is the daily rainfall data. In this paper, we present a novel…

Methodology · Statistics 2021-06-17 Sai K. Popuri , Nagaraj K. Neerchal , Amita Mehta , Ahmad Mousavi

We propose a class of weighted $L_2$-type tests of fit to the Gamma distribution. Our novel procedure is based on a fixed point property of a new transformation connected to a Steinian characterization of the family of Gamma distributions.…

Methodology · Statistics 2020-02-25 Steffen Betsch , Bruno Ebner

In this paper, we consider the problem of estimating Tsallis entropy from a given data set. We propose four different estimators for Tsallis entropy measure based on higher-order sample spacings, and then discuss estimation of Tsallis…

Methodology · Statistics 2026-02-10 Siddhartha Chakraborty , Asok K. Nanda , Narayanaswamy Balakrishnan

We consider the two-dimensional (2d) Ising model on a infinitely long cylinder and study the probabilities $p_i$ to observe a given spin configuration $i$ along a circular section of the cylinder. These probabilities also occur as…

Strongly Correlated Electrons · Physics 2010-11-02 Jean-Marie Stéphan , Grégoire Misguich , Vincent Pasquier