Matrix factorization is an important mathematical problem encountered in the context of
dictionary learning, recommendation systems, and machine learning. We introduce a …

Matrix factorization is an inference problem that has acquired importance due to its vast
range of applications that go from dictionary learning to recommendation systems and …

We consider increasingly complex models of matrix denoising and dictionary learning in the
Bayes-optimal setting, in the challenging regime where the matrices to infer have a rank …

In this manuscript we consider denoising of large rectangular matrices: given a noisy
observation of a signal matrix, what is the best way of recovering the signal matrix itself? For …

High-dimensional signal recovery of standard linear regression is a key challenge in many
engineering fields, such as, communications, compressed sensing, and image processing …

The inference of a large symmetric signal-matrix S∈ RN× N corrupted by additive Gaussian
noise, is considered for two regimes of growth of the rank M as a function of N. For sub-linear …

We propose a rectangular rotational invariant estimator to recover a real matrix from noisy
matrix observations coming from an arbitrary additive rotational invariant perturbation, in the …

We consider a statistical model for matrix factorization in a regime where the rank of the two
hidden matrix factors grows linearly with their dimension and their product is corrupted by …

Message-passing algorithms based on the belief propagation (BP) equations constitute a
well-known distributed computational scheme. They yield exact marginals on tree-like …

We consider the additive version of the matrix denoising problem, where a random
symmetric matrix $ S $ of size $ n $ has to be inferred from the observation of $ Y= S+ Z …