## Bernoulli

- Bernoulli
- Volume 20, Number 1 (2014), 282-303.

### Noisy low-rank matrix completion with general sampling distribution

#### Abstract

In the present paper, we consider the problem of matrix completion with noise. Unlike previous works, we consider quite general sampling distribution and we do not need to know or to estimate the variance of the noise. Two new nuclear-norm penalized estimators are proposed, one of them of “square-root” type. We analyse their performance under high-dimensional scaling and provide non-asymptotic bounds on the Frobenius norm error. Up to a logarithmic factor, these performance guarantees are minimax optimal in a number of circumstances.

#### Article information

**Source**

Bernoulli, Volume 20, Number 1 (2014), 282-303.

**Dates**

First available in Project Euclid: 22 January 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.bj/1390407290

**Digital Object Identifier**

doi:10.3150/12-BEJ486

**Mathematical Reviews number (MathSciNet)**

MR3160583

**Zentralblatt MATH identifier**

06282552

**Keywords**

high-dimensional sparse model low rank matrix estimation matrix completion unknown variance

#### Citation

Klopp, Olga. Noisy low-rank matrix completion with general sampling distribution. Bernoulli 20 (2014), no. 1, 282--303. doi:10.3150/12-BEJ486. https://projecteuclid.org/euclid.bj/1390407290