Abstract
Given a noisy measurement of a product of two matrices, the matrix factorization problem is to estimate back the original matrices. It arises in many applications such as dictionary learning, blind matrix calibration, sparse principal component analysis, blind source separation, low rank matrix completion, robust principal component analysis or factor analysis. We use the tools of statistical mechanics - the cavity and replica methods - to analyze the achievability and tractability of the inference problems in the setting of Bayes-optimal inference. Joint work with Lenka Zdeborova and Thibault Lesieur.