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

Christos Pelekis (1) , Jan Ramon (2) , Yuyi Wang (3)

1 KU Leuven - Catholic University of Leuven = Katholieke Universiteit Leuven
2 MAGNET - Machine Learning in Information Networks
3 NIGPAS-CAS - Nanjing Institute of Geology and Palaeontology

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.

Mots clés: Fractional chromatic number; Finner's inequality; Hypergraphs; Dependency graph; Janson's inequality

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

Christos Pelekis, Jan Ramon, Yuyi Wang. Hölder-type inequalities and their applications to concentration and correlation bounds. Indagationes Mathematicae, 2017, 28 (1), pp.170-182. ⟨10.1016/j.indag.2016.11.017⟩. ⟨hal-01421953⟩