Title :

Hölder-type inequalities and their applications to concentration and correlation bounds

Author(s) :

Pelekis, Christos [Auteur]
Catholic University of Leuven = Katholieke Universiteit Leuven [KU Leuven]
Ramon, Jan [Auteur]
Machine Learning in Information Networks [MAGNET]
Wang, Yuyi [Auteur]
Nanjing Institute of Geology and Palaeontology [NIGPAS-CAS]

Journal title :

Indagationes Mathematicae

Pages :

170–182

Publisher :

Elsevier

Publication date :

2017

ISSN :

0019-3577

English keyword(s) :

Fractional chromatic number
Finner's inequality
Hypergraphs
Dependency graph
Janson's inequality

HAL domain(s) :

Physique [physics]/Physique [physics]/Analyse de données, Statistiques et Probabilités [physics.data-an]
Informatique [cs]/Intelligence artificielle [cs.AI]
Informatique [cs]/Théorie de l'information [cs.IT]
Mathématiques [math]/Statistiques [math.ST]
Statistiques [stat]/Machine Learning [stat.ML]

English abstract : [en]

Let Y v , v ∈ V , be real-valued random variables having a dependency graph G = (V, E). We show that E ⎡ ⎣ ∏ v∈V Y v ⎤ ⎦ ≤ ∏ v∈V { E [ Y χ b b v ]} b χ b , where χ b is the b-fold chromatic number of G. This inequality may ...
Show more >Let Y v , v ∈ V , be real-valued random variables having a dependency graph G = (V, E). We show that E ⎡ ⎣ ∏ v∈V Y v ⎤ ⎦ ≤ ∏ v∈V { E [ Y χ b b v ]} b χ b , where χ b is the b-fold chromatic number of G. This inequality may be seen as a dependency-graph analogue of a generalised Hölder inequality, due to Helmut Finner. Additionally, we provide applications of the aforementioned Hölder-type inequalities to concentration and correlation bounds for sums of weakly dependent random variables whose dependencies can be described in terms of graphs or hypergraphs.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

Collections :

• Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189

Source :

Harvested from HAL