Binary graphical models with mean-field interactions: community detection and dependence graph density estimation

par Prof. Guilherme Ost (Federal University of Rio de Janeiro)

mardi 4 févr. 2025, 14:00 → 15:00 Europe/Paris

We consider a system of binary interacting chains describing the dynamics of a group of N individuals that, at each time unit, either send some signal to the others or remain silent otherwise. The interactions among the chains are encoded by a directed Erdös-Rényi random graph with unknown parameter 0<p<1. Moreover, the system is structured within two populations (excitatory chains versus inhibitory ones) which are coupled via a mean field interaction on the underlying Erdös-Rényi graph. These two populations are also unknown. In the first part of this talk, we will discuss how one can exactly discriminate the excitatory chains from the inhibitory ones based only on the observation of the interacting chains over T time units. In the second part of the talk, we then will address the question of inferring  the connectivity parameter p . If time allows, I will highlight some of the probabilistics tools we used to tackle both problems. The results presented are based on joint works with Eva Löcherbach (Paris 1) and Julien Chevallier (Grenoble).