In high-dimensional linear regression, the goal pursued here is to estimate an unknown regression function using linear combinations of a suitable set of covariates. One of the key assumptions forâ€¦ (More)

We perform a finite sample analysis of the detection levels for sparse principal components of a high-dimensional covariance matrix. Our minimax optimal test is based on a sparse eigenvalueâ€¦ (More)

In the context of sparse principal component detection, we bring evidence towards the existence of a statistical price to pay for computational efficiency. We measure the performance of a test by theâ€¦ (More)

Given a collection of M different estimators or classifiers, we study the problem of model selection type aggregation, i.e., we construct a new estimator or classifier, called aggregate, which isâ€¦ (More)

We consider semi-supervised classification when part of the available data is unlabeled. These unlabeled data can be useful for the classification problem when we make an assumption relating theâ€¦ (More)

In a regression setup with deterministic design, we study the pure aggregation problem and introduce a natural extension from the Gaussian distribution to distributions in the exponential family.â€¦ (More)

In the context of density level set estimation, we study the convergence of general plug-in methods under two main assumptions on the density for a given level Î». More precisely, it is assumed thatâ€¦ (More)

Consider a regression model with fixed design and Gaussian noise where the regression function can potentially be well approximated by a function that admits a sparse representation in a givenâ€¦ (More)

In the context of sparse principal component detection, we bring evidence towards the existence of a statistical price to pay for computational efficiency. We measure the performance of a test by theâ€¦ (More)

We consider a multi-armed bandit problem in a setting where each arm produces a noisy reward realization which depends on an observable random covariate. As opposed to the traditional staticâ€¦ (More)