Related papers: Sharp Oracle Inequalities for Low-complexity Prior…

We consider the sparse regression model where the number of parameters $p$ is larger than the sample size $n$. The difficulty when considering high-dimensional problems is to propose estimators achieving a good compromise between…

We build a unifying convex analysis framework characterizing the statistical properties of a large class of penalized estimators, both under a regular and an irregular design. Our framework interprets penalized estimators as proximal…

We build penalized least-squares estimators using the slope heuristic and resampling penalties. We prove oracle inequalities for the selected estimator with leading constant asymptotically equal to 1. We compare the practical performances…

We consider the problem of model selection type aggregation in the context of density estimation. We first show that empirical risk minimization is sub-optimal for this problem and it shares this property with the exponential weights…

In this note, we consider the problem of aggregation of estimators in order to denoise a signal. The main contribution is a short proof of the fact that the exponentially weighted aggregate satisfies a sharp oracle inequality. While this…

The paper focuses on the automatic selection of the grouped explanatory variables in an high-dimensional model, when the model errors are asymmetric. After introducing the model and notations, we define the adaptive group LASSO expectile…

We study high-dimensional linear models and the $\ell_1$-penalized least squares estimator, also known as the Lasso estimator. In literature, oracle inequalities have been derived under restricted eigenvalue or compatibility conditions. In…

We propose a general family of algorithms for regression estimation with quadratic loss. Our algorithms are able to select relevant functions into a large dictionary. We prove that a lot of algorithms that have already been studied for this…

This paper consider penalized empirical loss minimization of convex loss functions with unknown non-linear target functions. Using the elastic net penalty we establish a finite sample oracle inequality which bounds the loss of our estimator…

It has been shown in literature that the Lasso estimator, or l1-penalized least squares estimator, enjoys good oracle properties. This paper examines which special properties of the l1-penalty allow for sharp oracle results, and then…

A general many quantiles + noise model is studied in the robust formulation (allowing non-normal, non-independent observations), where the identifiability requirement for the noise is formulated in terms of quantiles rather than the…

We consider the problem of automatic variable selection in a linear model with asymmetric or heavy-tailed errors when the number of explanatory variables diverges with the sample size. For this high-dimensional model, the penalized least…

We consider the problem of estimating a sparse linear regression vector $\beta^*$ under a gaussian noise model, for the purpose of both prediction and model selection. We assume that prior knowledge is available on the sparsity pattern,…

We study the complexity of heavy-tailed sampling and present a separation result in terms of obtaining high-accuracy versus low-accuracy guarantees i.e., samplers that require only $O(\log(1/\varepsilon))$ versus…

Through the direct study of the analysis estimator we derive oracle inequalities with fast and slow rates by adapting the arguments involving projections by Dalalyan, Hebiri and Lederer (2017). We then extend the theory to the square root…

Partial penalized tests provide flexible approaches to testing linear hypotheses in high dimensional generalized linear models. However, because the estimators used in these tests are local minimizers of potentially non-convex…

We propose a new approach, along with refinements, based on $L_1$ penalties and aimed at jointly estimating several related regression models. Its main interest is that it can be rewritten as a weighted lasso on a simple transformation of…

We analyze general model selection procedures using penalized empirical loss minimization under computational constraints. While classical model selection approaches do not consider computational aspects of performing model selection, we…

The Lasso has attracted the attention of many authors these last years. While many efforts have been made to prove that the Lasso behaves like a variable selection procedure at the price of strong (though unavoidable) assumptions on the…

We study the problem of estimating multiple linear regression equations for the purpose of both prediction and variable selection. Following recent work on multi-task learning Argyriou et al. [2008], we assume that the regression vectors…