Convex optimization for matrix completion with application to forecasting

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Gillard, Jonathan | Usevich, Konstantin

Edité par CCSD -

Published in AIP Conference Proceedings 2070:020042, 2019. International audience. 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.

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