Convex optimization for matrix completion with application to forecasting
Résumé
We consider convex relaxations for the low-rank matrix completion problem with specific application to forecasting time series and consider how close the solution of the convex relaxed low-rank matrix completion problem is to the original global optimization problem. This is a fashionable approach in the statistics of big data, difficult non-convex optimization problems are ‘convexified’ to make them tractable. The question then is: how close is the solution of the convex optimization problem to the non-convex one (which is the one we really want to solve)? We consider a matrix completion problem for Hankel matrices and investigate some cases when the proposed approach can work through theoretical and empirical results.