19 citations · 121 across the 22 of their papers we have counts for
5 papers · 1 filter
Bounds on the prediction error of penalized least squares estimators with convex penalty
Pierre C. Bellec, Alexandre B. Tsybakov
This paper considers the penalized least squares estimator with arbitrary convex penalty. When the observation noise is Gaussian, we show that the prediction error is a subgaussian…
On the prediction loss of the lasso in the partially labeled setting
Pierre C. Bellec, Arnak S. Dalalyan, Edwin Grappin +1
In this paper we revisit the risk bounds of the lasso estimator in the context of transductive and semi-supervised learning. In other terms, the setting under consideration is that…
Slope meets Lasso: improved oracle bounds and optimality
Pierre C. Bellec, Guillaume Lecué, Alexandre B. Tsybakov
We show that two polynomial time methods, a Lasso estimator with adaptively chosen tuning parameter and a Slope estimator, adaptively achieve the exact minimax prediction and $\ell…
Aggregation of supports along the Lasso path
Pierre C. Bellec
In linear regression with fixed design, we propose two procedures that aggregate a data-driven collection of supports. The collection is a subset of the possible supports and…
Adaptive confidence sets in shape restricted regression
Pierre C. Bellec
A simple construction of adaptive confidence sets is proposed in isotonic, convex and unimodal regression. In univariate isotonic regression, the proposed confidence set enjoys uni…