Hölder-type inequalities and their ...
Document type :
Compte-rendu et recension critique d'ouvrage
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]
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
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]
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 >
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
Popular science :
Non
Collections :
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