Phase transitions in low-rank matrix estimation

par Léo Miolane (ENS Paris)

jeudi 23 mars 2017, 14:30 → 15:30 Europe/Paris

salle 435 (UMPA)

We consider the estimation of noisy low-rank matrices. We compute the minimal mean square error (MMSE) for this statistical problem. We will observe a phase transition: there exists a critical value of the signal-to-noise ratio above which it is possible to make a non-trivial guess about the signal, whereas this is impossible below this critical value. We will see that this problem reduces to the study of a spin glass system. We will show that this system enjoys specific properties, because it arises from a statistical problem. Using these properties and tools from the study of spin glasses, we compute limiting expressions for the free energy and the MMSE. (joint work with Marc Lelarge)