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Related papers: Weighted information and entropy rates

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Let $X$ be a discrete random variable with support $S$ and $f : S \to S^\prime$ be a bijection. Then it is well-known that the entropy of $X$ is the same as the entropy of $f(X)$. This entropy preservation property has been well-utilized to…

Information Theory · Computer Science 2007-07-13 Chandra Nair , Balaji Prabhakar , Devavrat Shah

We present a new method of estimating the dispersion of a distribution which is based on the surprising property of a function that measures information processing intensity. It turns out that this function has a maximum at its fixed point.…

Data Analysis, Statistics and Probability · Physics 2015-06-19 Rober Jankowski , Marcin Makowski , Edward W. Piotrowski

Entropy and information provide natural measures of correlation among elements in a network. We construct here the information theoretic analog of connected correlation functions: irreducible $N$--point correlation is measured by a decrease…

Biological Physics · Physics 2016-09-08 Elad Schneidman , Susanne Still , Michael J. Berry , William Bialek

In this paper, I try to tame "Basu's elephants" (data with extreme selection on observables). I propose new practical large-sample and finite-sample methods for estimating and inferring heterogeneous causal effects (under unconfoundedness)…

Econometrics · Economics 2023-01-20 Ganesh Karapakula

Behavioural economics provides labels for patterns in human economic behaviour. Probability weighting is one such label. It expresses a mismatch between probabilities used in a formal model of a decision (i.e. model parameters) and…

Theoretical Economics · Economics 2020-05-04 Ole Peters , Alexander Adamou , Mark Kirstein , Yonatan Berman

Based on the canonical correlation analysis we derive series representations of the probability density function (PDF) and the cumulative distribution function (CDF) of the information density of arbitrary Gaussian random vectors as well as…

Information Theory · Computer Science 2022-07-13 Jonathan Huffmann , Martin Mittelbach

Entropies are fundamental measures of uncertainty with central importance in information theory and statistics and applications across all the quantitative sciences. Under a natural set of operational axioms, the most general form of…

Information Theory · Computer Science 2026-02-02 Roberto Rubboli , Erkka Haapasalo , Marco Tomamichel

The notion of probability density for a random function is not as straightforward as in finite-dimensional cases. While a probability density function generally does not exist for functional data, we show that it is possible to develop the…

Statistics Theory · Mathematics 2010-03-01 Aurore Delaigle , Peter Hall

We discuss the generalized von Neumann (Tsallis) entropy and the generalized Fisher information (GFI) in nonextensive quantum systems, by using the interpolation approximation (IA) which has been shown to yield good results for the quantal…

Statistical Mechanics · Physics 2009-09-22 Hideo Hasegawa

We provide a new expression of the quantum Fisher information(QFI) for a general system. Utilizing this expression, the QFI for a non-full rank density matrix is only determined by its support. This expression can bring convenience for a…

Quantum Physics · Physics 2014-01-31 Jing Liu , Xiao-Xing Jing , Wei Zhong , Xiaoguang Wang

Wyner's common information was originally defined for a pair of dependent discrete random variables. Its significance is largely reflected in, hence also confined to, several existing interpretations in various source coding problems. This…

Information Theory · Computer Science 2013-01-11 Ge Xu , Wei Liu , Biao Chen

In a previous paper, we introduced an axiomatic system for information thermodynamics, deriving an entropy function that includes both thermodynamic and information components. From this function we derived an entropic probability…

Quantum Physics · Physics 2024-12-18 Benjamin Schumacher , Michael D. Westmoreland

A probabilistic source is defined as the set of infinite words (over a given denumerable alphabet) endowed with a probability $\mu$. The paper deals with general binary sources where the distribution of any symbol (0 or 1) may depend on an…

Dynamical Systems · Mathematics 2025-04-07 Ali Akhavi , Eda Cesaratto , Frédéric Paccaut , Pablo Rotondo , Brigitte Vallée

The lifetime of a system of connected units under some natural assumptions can be represented as a random variable Y defined as a weighted lattice polynomial of random lifetimes of its components. As such, the concept of a random variable Y…

Probability · Mathematics 2008-05-28 Alexander Dukhovny , Jean-Luc Marichal

As the world is becoming more dependent on the internet for information exchange, some overzealous journalists, hackers, bloggers, individuals and organizations tend to abuse the gift of free information environment by polluting it with…

Computation and Language · Computer Science 2021-04-02 Kwadwo Osei Bonsu

Goal of these proceedings is to introduce a method based on event weighting in particle physics experiments. Weighting means that events are not just counted as integer numbers but are assigned a weight factor according to their importance…

Data Analysis, Statistics and Probability · Physics 2022-03-11 Joerg Pretz

We establish a variant of the log-Sobolev and transport-information inequalities for mixture distributions. If a probability measure $\pi$ can be decomposed into components that individually satisfy such inequalities, then any measure $\mu$…

Information Theory · Computer Science 2026-03-16 Jonathan Niles-Weed

A fundamental task in the analysis of datasets with many variables is screening for associations. This can be cast as a multiple testing task, where the objective is achieving high detection power while controlling type I error. We consider…

Methodology · Statistics 2021-09-01 Nikolaos Ignatiadis , Wolfgang Huber

We propose a novel approach framed in terms of information theory and entropy to tackle the issue of conspiracy theories propagation. We start with the report of an event (such as 9/11 terroristic attack) represented as a series of…

Physics and Society · Physics 2015-10-28 Natasa Golo , Serge Galam

The generalized weighted mean operator $\mathbf{M}^{g}_{w}$ is given by $$[\mathbf{M}^{g}_{w}f](x)= g^{-1}\left(\frac{1}{W(x)}\int_{0}^{x}w(t)g(f(t))\,\mathrm{d}t\right),$$ with $$W(x)=\int_{0}^{x} w(s)\,\mathrm{d}s, \quad \textrm{for} x…

Probability · Mathematics 2013-09-24 Ondrej Hutník