Constructing confidence sets for the matrix completion problem

Alexandra Carpentier (1) , Olga Klopp (2, 3) , Matthias Löffler (4)

1 University of Potsdam = Universität Potsdam
2 CREST - Centre de Recherche en Économie et Statistique
3 MODAL'X - Modélisation aléatoire de Paris X
4 CAM - University of Cambridge [UK]

In the present note we consider the problem of constructing honest and adaptive confidence sets for the matrix completion problem. For the Bernoulli model with known variance of the noise we provide a realizable method for constructing confidence sets that adapt to the unknown rank of the true matrix.

Mots clés: adaptivity; matrix completion; low rank recovery; confidence sets

Domaines: Statistiques [math.ST]

Alexandra Carpentier, Olga Klopp, Matthias Löffler. Constructing confidence sets for the matrix completion problem. 2017. ⟨hal-01504257⟩