Appears in collection : Les probabilités de demain 2017

Joint work with Marc Lelarge We consider the estimation of noisy low-rank matrices. Our goal is to 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.