Statistical Hypothesis Testing Based on Machine Learning: Large Deviations Analysis

Autor: Paolo Braca, Leonardo M. Millefiori, Augusto Aubry, Stefano Marano, Antonio De Maio, Peter Willett

Publikováno v: IEEE Open Journal of Signal Processing, Vol 3, Pp 464-495 (2022)

We study the performance of Machine Learning (ML) classification techniques. Leveraging the theory of large deviations, we provide the mathematical conditions for a ML classifier to exhibit error probabilities that vanish exponentially, say $\exp (-n

Externí odkaz: https://doaj.org/article/dbfaf65ed2604742a1d01e9e79807588

Dynamic Hilbert-Type Inequalities with Fenchel-Legendre Transform

Autor: Ahmed A. El-Deeb, Samer D. Makharesh, Dumitru Baleanu

Publikováno v: Symmetry, Vol 12, Iss 4, p 582 (2020)

Our work is based on the multiple inequalities illustrated in 2020 by Hamiaz and Abuelela. With the help of a Fenchel-Legendre transform, which is used in various problems involving symmetry, we generalize a number of those inequalities to a general

Externí odkaz: https://doaj.org/article/c92f9457f9a246719c9a518e70d9aa62

Integral inequalities of Hilbert's type involving Fenchel-Legendre transform with applications

Autor: Waleed Abuelela, Adnane Hamiaz, G. M. Bahaa

Publikováno v: Journal of Taibah University for Science, Vol 13, Iss 1, Pp 390-395 (2019)

New integral inequalities of Hilbert's type are introduced through Fenchel-Legendre transform. Some of these inequalities are considered as generalizations as well as improvements of some previously proved results. Applications of the extracted inequ

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4ce3fef000c5d37a8dcd27ffc92e148d
https://doi.org/10.1080/16583655.2019.1579952

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An estimation method for the chi-square divergence with application to test of hypotheses

Autor: Broniatowski, Michel, Leorato, Samantha

Publikováno v: Journal of Multivariate Analysis
Journal of Multivariate Analysis, Elsevier, 2016, 97 (6), pp.409-1436
Journal of Multivariate Analysis, 2016, 97 (6), pp.409-1436

We propose a new definition of the chi-square divergence between distributions. Based on convexity properties and duality, this version of the {\chi}^2 is well suited both for the classical applications of the {\chi}^2 for the analysis of contingency

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::89e8fa04f4c75136b920fba4e1f9cfaf
https://hal.archives-ouvertes.fr/hal-00555139/file/HAL12012011.pdf