Noisy low-rank matrix completion with general sampling distribution

Olga Klopp (1)

1 CREST - Centre de Recherche en Économie et Statistique

In the present paper we consider the problem of matrix completion with noise for general sampling schemes. Unlike previous works, in our construction we do not need to know or to evaluate the sampling distribution or the variance of the noise. We propose new nuclear-norm penalized estimators, one of them of the ''square-root'' type. We prove that, up to a logarithmic factor, our estimators achieve optimal rates with respect to the estimation error.

Mots clés: matrix completion; low rank matrix estimation; unknown variance; high-dimensional sparse model

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Olga Klopp. Noisy low-rank matrix completion with general sampling distribution. Bernoulli, 2014, 20 (1), pp.282--303. ⟨hal-00675413v2⟩