Section: New Results

Statistical Learning on Graphs

The main purpose of [11] is to illustrate that certain Hölder-type inequalities can be employed in order to obtain concentration and correlation bounds for sums of weakly dependent random variables whose dependencies are described in terms of graphs, or hypergraphs. Let $Y_v$ , $v\in V$, be real-valued random variables having a dependency graph $G=(V,E)$. We show that

where ${\chi }_b$ is the $b$-fold chromatic number of $G$. This inequality may be seen as a dependency-graph analogue of a generalized 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.

Several collaborations concerned efficient counting of subgraph frequencies in networks. Two journal articles are accepted subject to minor revisions, one in collaboration with the group of Yvan Saeys (University of Ghent, Belgium), and one in collaboration with Irma Ravkic and Martin Znidarsic (former collaborators of Jan Ramon ).