Section: New Results

Probabilistic low-rank matrix completion with adaptive spectral regularization algorithms

Participants : Marie Chavent, Adrien Todeschini.

We propose a novel class of algorithms for low rank matrix completion. Our approach builds on novel penalty functions on the singular values of the low rank matrix. By exploiting a mixture model representation of this penalty, we show that a suitably chosen set of latent variables enables to derive an EM algorithm to obtain a Maximum A Posteriori estimate of the completed low rank matrix. The resulting algorithm is an iterative soft-thresholded algorithm which iteratively adapts the shrinkage coefficients associated to the singular values.

This work is in collaboration with Francois Caron from University of Oxford. It has been presented in the national conference of the French Statistical Society of Statistics [41]