Summary Sampling from various kinds of distribution is an issue paramount importance in statistics since it often the key ingredient for constructing estimators, test procedures or confidence intervals. In many situations, exact sampling a given impossible computationally expensive and, therefore, one needs to resort approximate strategies. However, there no well-developed theory providing meaningful non-asymptotic guarantees procedures, especially high dimensional problems. The paper makes...

Although the Lasso has been extensively studied, relationship between its prediction performance and correlations of covariates is not fully understood. In this paper, we give new insights into in context multiple linear regression. We show, particular, that incorporation a simple correlation measure tuning parameter can lead to nearly optimal even for highly correlated covariates. However, also reveal moderately covariates, be mediocre irrespective choice parameter. finally show our results...

In recent years, overcomplete dictionaries combined with sparse learning techniques became extremely popular in computer vision. While their usefulness is undeniable, the improvement they provide specific tasks of vision still poorly understood. The aim present work to demonstrate that for task image denoising, nearly state-of-the-art results can be achieved using orthogonal only, provided are learned directly from noisy image. To this end, we introduce three patchbased denoising algorithms...

Langevin diffusion processes and their discretizations are often used for sampling from a target density. The most convenient framework assessing the quality of such scheme corresponds to smooth strongly log-concave densities defined on $\mathbb{R}^{p}$. present work focuses this studies behavior Monte Carlo algorithm based kinetic diffusion. We first prove geometric mixing property with rate that is optimal in terms its dependence condition number. then use result obtaining improved...

We address the issue of variable selection in regression model with very high ambient dimension, that is, when number variables is large. The main focus on situation where relevant variables, called intrinsic much smaller than dimension $d$. Without assuming any parametric form underlying function, we get tight conditions making it possible to consistently estimate set variables. These relate and sample size. procedure provably consistent under these based comparing quadratic functionals...

In this paper, we revisit the recently established theoretical guarantees for convergence of Langevin Monte Carlo algorithm sampling from a smooth and (strongly) log-concave density. We improve existing results when is measured in Wasserstein distance provide further insights on very tight relations between, one hand, and, other gradient descent optimization. Finally, also establish version that based noisy evaluations gradient.

We consider the problem of combining a (possibly uncountably infinite) set affine estimators in nonparametric regression model with heteroscedastic Gaussian noise. Focusing on exponentially weighted aggregate, we prove PAC-Bayesian type inequality that leads to sharp oracle inequalities discrete but also continuous settings. The framework is general enough cover combinations various procedures such as least square regression, kernel ridge shrinking and many other used literature statistical...

We consider the problem of aggregating elements a possibly infinite dictionary for building decision procedure that aims at minimizing given criterion. Along with dictionary, an independent identically distributed training sample is available, on which performance can be tested. In fairly general set-up, we establish oracle inequality Mirror Averaging aggregate any prior distribution. By choosing appropriate prior, apply this in context prediction under sparsity assumption problems...

The statistical problem of estimating the effective dimension-reduction (EDR) subspace in multi-index regression model with deterministic design and additive noise is considered. A new procedure for recovering directions EDR proposed. Under mild assumptions, $\sqrt n$-consistency proposed proved (up to a logarithmic factor) case when structural dimension not larger than 4. empirical behavior algorithm studied through numerical simulations.

We consider the problem of testing a particular type composite null hypothesis under nonparametric multivariate regression model. For given quadratic functional $Q$, states that function $f$ satisfies constraint $Q[f]=0$, while alternative corresponds to functions for which $Q[f]$ is bounded away from zero. On one hand, we provide minimax rates and exact separation constants, along with sharp-optimal procedure, diagonal nonnegative functionals. smoothness classes ellipsoidal form check our...

In this paper, we consider the problem of estimating covariation two diffusion processes when observations are subject to non-synchronicity. Building on recent papers \cite{Hay-Yos03, Hay-Yos04}, derive second-order asymptotic expansions for distribution Hayashi-Yoshida estimator in a fairly general setup including random sampling schemes and non-anticipative drifts. The key steps leading our results decomposition estimator's Gaussian set-up, stochastic itself an accurate evaluation...

In this paper we revisit the risk bounds of lasso estimator in context transductive and semi-supervised learning. other terms, setting under consideration is that regression with random design partial labeling. The main goal to obtain user-friendly on off-sample prediction risk. To end, simple bounded response variable (high-dimensional) covariates considered. We propose some new adaptations these settings establish oracle inequalities both expectation deviation. These results provide...

The problem of matching two sets features appears in various tasks computer vision and can be often formalized as a permutation estimation. We address this from statistical point view provide theoretical analysis the accuracy several natural estimators. To end, minimax rate separation is investigated its expression obtained function sample size, noise level dimension. consider cases homoscedastic heteroscedastic establish, each case, tight upper bounds on distance These are shown to...