English
Related papers

Related papers: A class of R\'{e}nyi information estimators for mu…

200 papers

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,…

Methodology · Statistics 2024-08-30 Brijesh P. Singh , Utpal Dhar Das

A comparative study of one-dimensional quantum structures which allow analytic expressions for the position and momentum R\'{e}nyi $R(\alpha)$ and Tsallis $T(\alpha)$ entropies, focuses on extracting the most characteristic physical…

Quantum Physics · Physics 2019-01-15 O. Olendski

The q-exponential distributions, which are generalizations of the Zipf-Mandelbrot power-law distribution, are frequently encountered in complex systems at their stationary states. From the viewpoint of the principle of maximum entropy, they…

Statistical Mechanics · Physics 2009-11-07 Sumiyoshi Abe

Estimating the Shannon entropy of a discrete distribution from which we have only observed a small sample is challenging. Estimating other information-theoretic metrics, such as the Kullback-Leibler divergence between two sparsely sampled…

Data Analysis, Statistics and Probability · Physics 2023-02-24 Angelo Piga , Lluc Font-Pomarol , Marta Sales-Pardo , Roger Guimerà

We propose a new way of defining entropy of a system, which gives a general form which may be nonextensive as Tsallis entropy, but is linearly dependent on component entropies, like Renyi entropy, which is extensive. This entropy has a…

Adaptation and Self-Organizing Systems · Physics 2007-10-11 Fariel Shafee

We demonstrate that a popular class of nonparametric mutual information (MI) estimators based on k-nearest-neighbor graphs requires number of samples that scales exponentially with the true MI. Consequently, accurate estimation of MI…

Information Theory · Computer Science 2015-03-09 Shuyang Gao , Greg Ver Steeg , Aram Galstyan

This paper studies the use of the Tsallis Entropy versus the classic Boltzmann-Gibbs-Shannon entropy for classifying image patterns. Given a database of 40 pattern classes, the goal is to determine the class of a given image sample. Our…

Data Analysis, Statistics and Probability · Physics 2011-12-30 Ricardo Fabbri , Wesley N. Gonçalves , Francisco J. P. Lopes , Odemir M. Bruno

Reliable data-driven estimation of Shannon entropy from small data sets, where the number of examples is potentially smaller than the number of possible outcomes, is a critical matter in several applications. In this paper, we introduce a…

Machine Learning · Computer Science 2025-12-12 Gabriel F. A. Bastos , Jugurta Montalvão

The new estimates of the conditional Shannon entropy are introduced in the framework of the model describing a discrete response variable depending on a vector of d factors having a density w.r.t. the Lebesgue measure in R^d. Namely, the…

Statistics Theory · Mathematics 2018-04-25 Alexander Bulinski , Alexey Kozhevin

Mixture distributions arise in many parametric and non-parametric settings -- for example, in Gaussian mixture models and in non-parametric estimation. It is often necessary to compute the entropy of a mixture, but, in most cases, this…

Information Theory · Computer Science 2022-11-22 Artemy Kolchinsky , Brendan D. Tracey

We consider a probability distribution depending on a real parameter $x$. As functions of $x$, the R\'enyi entropy and the Tsallis entropy can be expressed in terms of the associated index of coincidence $S(x)$. We establish recurrence…

Classical Analysis and ODEs · Mathematics 2019-10-31 Alexandra Maduta , Diana Otrocol , Ioan Rasa

It was recently shown that estimating the Shannon entropy $H({\rm p})$ of a discrete $k$-symbol distribution ${\rm p}$ requires $\Theta(k/\log k)$ samples, a number that grows near-linearly in the support size. In many applications $H({\rm…

Information Theory · Computer Science 2016-03-11 Jayadev Acharya , Alon Orlitsky , Ananda Theertha Suresh , Himanshu Tyagi

We consider nonparametric estimation of $L_2$, Renyi-$\alpha$ and Tsallis-$\alpha$ divergences between continuous distributions. Our approach is to construct estimators for particular integral functionals of two densities and translate them…

Machine Learning · Statistics 2014-05-13 Akshay Krishnamurthy , Kirthevasan Kandasamy , Barnabas Poczos , Larry Wasserman

Images obtained from coherent illumination processes are contaminated with speckle noise, with polarimetric synthetic aperture radar (PolSAR) imagery as a prominent example. With an adequacy widely attested in the literature, the scaled…

Methodology · Statistics 2015-06-11 Alejandro C. Frery , Renato J. Cintra , Abraão D. C. Nascimento

We consider the problem of estimating a density $f_X$ using a sample $Y_1,...,Y_n$ from $f_Y=f_X\star f_{\epsilon}$, where $f_{\epsilon}$ is an unknown density. We assume that an additional sample $\epsilon_1,...,\epsilon_m$ from…

Statistics Theory · Mathematics 2009-08-21 Jan Johannes

We propose a new density estimation algorithm. Given $n$ i.i.d. observations from a distribution belonging to a class of densities on $\mathbb{R}^d$, our estimator outputs any density in the class whose "perceptron discrepancy" with the…

Statistics Theory · Mathematics 2025-06-09 Patrik Róbert Gerber , Tianze Jiang , Yury Polyanskiy , Rui Sun

In this work, we investigate the reliability of information-theoretic measures based on the electron-density and shape-function, specifically Shannon and R\'enyi entropies, as descriptors of electronic correlation. By establishing a…

Quantum Physics · Physics 2026-05-21 Diogo J. L. Rodrigues , Evelio Francisco , Ángel Martín Pendás

We study the estimation of Tsallis entropy of a finite number of independent populations, each following an exponential distribution with the same scale parameter and distinct location parameters for $q>0$. We derive a Stein-type improved…

Statistics Theory · Mathematics 2024-01-18 Naveen Kumar , Ambesh Dixit , Vivek Vijay

We conclude a sequence of work by giving near-optimal sketching and streaming algorithms for estimating Shannon entropy in the most general streaming model, with arbitrary insertions and deletions. This improves on prior results that obtain…

Data Structures and Algorithms · Computer Science 2008-12-18 Nicholas J. A. Harvey , Jelani Nelson , Krzysztof Onak

We present a local density estimator based on first order statistics. To estimate the density at a point, $x$, the original sample is divided into subsets and the average minimum sample distance to $x$ over all such subsets is used to…

Methodology · Statistics 2014-12-10 Vikram V. Garg , Luis Tenorio , Karen Willcox