The Markov Random Geometric Graph: A growth model for temporal dynamic networks
Séminaire Données et Aléatoire Théorie & Applications
16/12/2021 - 14:00 Quentin Duchemin (LAMA http://lama.u-pem.fr/membres/duchemin.quentin) Salle 106 - https://www-ljk.imag.fr/membres/Julien.Chevallier/seminaire.html
In this talk, I will present the Markov Random Geometric Graphs (MRGGs), a growth model for temporal dynamic networks. It is based on a Markovian latent space dynamic: consecutive latent points are sampled on the Euclidean Sphere using an unknown Markov kernel; and two nodes are connected with a probability depending on a unknown function of their latent geodesic distance. With my PhD supervisors, we proved theoretical guarantees for the non-parametric estimation of the Markov kernel and the connection function. Proofs encompass concentration inequalities for random matrices and a recent concentration inequality for U-statistics of order 2 in a dependent framework. As a by product, we propose heuristics to solve link prediction tasks.