Group lasso estimation of high-dimensional covariance matrices

We extend our sharp minimax results in different directions: first, to Gaussian matrices with unknown variance, next, to matrices of random variables having a distribution from

In this paper we focus on the problem of high-dimensional matrix estimation from noisy observations with unknown variance of the noise.. Our main interest is the high

Moreover, our results are the first to give for this problem an analysis of penalization (such nuclear norm penalization) as a regularization algorithm: our oracle inequalities

In order to prove Theorem 1.1 we shall split the operator into a sum of operators which will behave as Weyl operators with respect to a first subset of the variables (meaning

To our knowledge there are only two non asymptotic results for the Lasso in logistic model : the first one is from Bach [2], who provided bounds for excess risk

To our knowledge there are only two non asymptotic results for the Lasso in logistic model: the first one is from Bach [2], who provided bounds for excess risk

However, employing this χ 2 limit distribution for dimensions like 30 or 40, increases dramatically the size of the test. The reason for this fail of classical LR test is the

Relying on recent advances in statistical estima- tion of covariance distances based on random matrix theory, this article proposes an improved covariance and precision