English
Related papers

Related papers: Complex-Valued Probability Measures and Their Appl…

200 papers

A new combinatorial-probabilistic diagnostic entropy has been introduced. It describes the pair-wise sum of probabilities of system conditions that have to be distinguished during the diagnosing process. The proposed measure describes the…

Information Theory · Computer Science 2009-09-29 Henryk Borowczyk

Logical entropy gives a measure, in the sense of measure theory, of the distinctions of a given partition of a set, an idea that can be naturally generalized to classical probability distributions. Here, we analyze how fundamental concepts…

Quantum Physics · Physics 2022-03-14 Boaz Tamir , Ismael L. Paiva , Zohar Schwartzman-Nowik , Eliahu Cohen

The profile of a sample is the multiset of its symbol frequencies. We show that for samples of discrete distributions, profile entropy is a fundamental measure unifying the concepts of estimation, inference, and compression. Specifically,…

Machine Learning · Statistics 2020-02-27 Yi Hao , Alon Orlitsky

An analysis of quantum measurement is presented that relies on an information-theoretic description of quantum entanglement. In a consistent quantum information theory of entanglement, entropies (uncertainties) conditional on measurement…

Quantum Physics · Physics 2008-02-03 N. J. Cerf , C. Adami

This thesis is a multidisciplinary contribution to the information theory of single-particle Coulomb systems in their relativistic and not relativistic description, to the theory of special functions of mathematical physics with the…

Quantum Physics · Physics 2011-03-18 Daniel Manzano

Tight bounds for several symmetric divergence measures are introduced, given in terms of the total variation distance. Each of these bounds is attained by a pair of 2 or 3-element probability distributions. An application of these bounds…

Information Theory · Computer Science 2016-11-15 Igal Sason

Quantum information theory, particularly its entropic formulations, has made remarkable strides in characterizing quantum systems and tasks. However, a critical dimension remains underexplored: computational efficiency. While classical…

Quantum Physics · Physics 2026-05-05 Noam Avidan , Thomas A. Hahn , Joseph M. Renes , Rotem Arnon

Importance sampling approximates expectations with respect to a target measure by using samples from a proposal measure. The performance of the method over large classes of test functions depends heavily on the closeness between both…

Computation · Statistics 2016-09-01 Daniel Sanz-Alonso

In this paper we introduce a nonextensive quantum information theoretic measure which may be defined between any arbitrary number of density matrices, and we analyze its fundamental properties in the spectral graph-theoretic framework.…

Information Theory · Computer Science 2015-04-15 A. Ben Hamza

The growing study of time series, especially those related to nonlinear systems, has challenged the methodologies to characterize and classify dynamical structures of a signal. Here we conceive a new diagnostic tool for time series based on…

Other Statistics · Statistics 2017-07-05 G. Corso , T. L. Prado , G. Z. dos S. Lima , S. R. Lopes

I present a framework based on the concepts of diversity and coherence for the analysis of knowledge integration and diffusion. Visualisations that help understand insights gained are also introduced. The key novelty offered by this…

Physics and Society · Physics 2014-12-23 Ismael Rafols

We consider probabilistic theories in which the most elementary system, a two-dimensional system, contains one bit of information. The bit is assumed to be contained in any complete set of mutually complementary measurements. The…

Quantum Physics · Physics 2009-07-10 Caslav Brukner , Anton Zeilinger

An information theoretic measure is derived that quantifies the statistical coherence between systems evolving in time. The standard time delayed mutual information fails to distinguish information that is actually exchanged from shared…

Chaotic Dynamics · Physics 2009-10-31 Thomas Schreiber

The entropy is a measure of uncertainty that plays a central role in information theory. When the distribution of the data is unknown, an estimate of the entropy needs be obtained from the data sample itself. We propose a semi-parametric…

Methodology · Statistics 2022-01-06 Stéphane Robin , Luca Scrucca

Based on the theory of quantum mechanics, intrinsic randomness in measurement distinguishes quantum effects from classical ones. From the perspective of states, this quantum feature can be summarized as coherence or superposition in a…

Quantum Physics · Physics 2017-04-03 Xiao Yuan , Hongyi Zhou , Zhu Cao , Xiongfeng Ma

The ability of quantum states to be in superposition is one of the key features that sets them apart from the classical world. This `coherence' is rigorously quantified by resource theories, which aim to understand how such properties may…

Quantum Physics · Physics 2024-07-08 Ruvi Lecamwasam , Syed M Assad , Joseph J Hope , Ping Koy Lam , Jayne Thompson , Mile Gu

Random probabilities are a key component to many nonparametric methods in Statistics and Machine Learning. To quantify comparisons between different laws of random probabilities several works are starting to use the elegant Wasserstein over…

Statistics Theory · Mathematics 2024-05-27 Marta Catalano , Hugo Lavenant

Although some information-theoretic measures of uncertainty or granularity have been proposed in rough set theory, these measures are only dependent on the underlying partition and the cardinality of the universe, independent of the lower…

Artificial Intelligence · Computer Science 2011-02-02 Ping Zhu , Qiaoyan Wen

Reliable estimation of predictive uncertainty is crucial for machine learning applications, particularly in high-stakes scenarios where hedging against risks is essential. Despite its significance, there is no universal agreement on how to…

Machine Learning · Computer Science 2025-06-17 Kajetan Schweighofer , Lukas Aichberger , Mykyta Ielanskyi , Sepp Hochreiter

In previous work, we presented a novel information-theoretic privacy criterion for query forgery in the domain of information retrieval. Our criterion measured privacy risk as a divergence between the user's and the population's query…

Information Theory · Computer Science 2015-03-19 David Rebollo-Monedero , Javier Parra-Arnau , Jordi Forné