172 citations · 763 across the 43 of their papers we have counts for
22 papers · 1 filter
Confidence envelopes for the false discoveries with heterogeneous data
Romain Périer, Gilles Blanchard, Sebastian Döhler +2
In the context of selective inference, confidence envelopes for the false discoveries allow the user to select any subset of null hypotheses while having a statistical guarantee on…
False discovery proportion envelopes with m-consistency
Iqraa Meah, Gilles Blanchard, Etienne Roquain
We provide new non-asymptotic false discovery proportion (FDP) confidence envelopes in several multiple testing settings relevant for modern high dimensional-data methods. We revis…
Constant regret for sequence prediction with limited advice
El Mehdi Saad, G. Blanchard
We investigate the problem of cumulative regret minimization for individual sequence prediction with respect to the best expert in a finite family of size K under limited access to…
On agnostic post hoc approaches to false positive control
Gilles Blanchard, Pierre Neuvial, Etienne Roquain
This document is a book chapter which gives a partial survey on post hoc approaches to false positive control.
Lepskii Principle in Supervised Learning
Gilles Blanchard, Peter Mathé, Nicole Mücke
In the setting of supervised learning using reproducing kernel methods, we propose a data-dependent regularization parameter selection rule that is adaptive to the unknown regulari…
Convergence analysis of Tikhonov regularization for non-linear statistical inverse learning problems
Abhishake Rastogi, Gilles Blanchard, Peter Mathé
We study a non-linear statistical inverse learning problem, where we observe the noisy image of a quantity through a non-linear operator at some random design points. We consider t…
Post hoc false positive control for spatially structured hypotheses
Guillermo Durand, Gilles Blanchard, Pierre Neuvial +1
In a high dimensional multiple testing framework, we present new confidence bounds on the false positives contained in subsets S of selected null hypotheses. The coverage probabili…
On the Post Selection Inference constant under Restricted Isometry Properties
François Bachoc, Gilles Blanchard, Pierre Neuvial
Uniformly valid confidence intervals post model selection in regression can be constructed based on Post-Selection Inference (PoSI) constants. PoSI constants are minimal for orthog…
Early stopping for statistical inverse problems via truncated SVD estimation
Gilles Blanchard, Marc Hoffmann, Markus Reiß
We consider truncated SVD (or spectral cut-off, projection) estimators for a prototypical statistical inverse problem in dimension . Since calculating the singular value decompo…
Post hoc inference via joint family-wise error rate control
Gilles Blanchard, Pierre Neuvial, Etienne Roquain
We introduce a general methodology for post hoc inference in a large-scale multiple testing framework. The approach is called "user-agnostic" in the sense that the statistical guar…
Minimax Euclidean Separation Rates for Testing Convex Hypotheses in
Gilles Blanchard, Alexandra Carpentier, Maurilio Gutzeit
We consider composite-composite testing problems for the expectation in the Gaussian sequence model where the null hypothesis corresponds to a convex subset of $\math…
Parallelizing Spectral Algorithms for Kernel Learning
Gilles Blanchard, Nicole Mücke
We consider a distributed learning approach in supervised learning for a large class of spectral regularization methods in an RKHS framework. The data set of size n is partitioned…
Convergence rates of Kernel Conjugate Gradient for random design regression
Gilles Blanchard, Nicole Krämer
We prove statistical rates of convergence for kernel-based least squares regression from i.i.d. data using a conjugate gradient algorithm, where regularization against overfitting…
Optimal adaptation for early stopping in statistical inverse problems
Gilles Blanchard, Marc Hoffmann, Markus Reiß
For linear inverse problems , it is classical to recover the unknown signal by iterative regularisation methods and halt at…
Optimal learning rates for Kernel Conjugate Gradient regression
Gilles Blanchard, Nicole Kraemer
We prove rates of convergence in the statistical sense for kernel-based least squares regression using a conjugate gradient algorithm, where regularization against overfitting is o…
Statistical performance of support vector machines
Gilles Blanchard, Olivier Bousquet, Pascal Massart
The support vector machine (SVM) algorithm is well known to the computer learning community for its very good practical results. The goal of the present paper is to study this algo…
Two simple sufficient conditions for FDR control
Gilles Blanchard, Etienne Roquain
We show that the control of the false discovery rate (FDR) for a multiple testing procedure is implied by two coupled simple sufficient conditions. The first one, which we call ``s…
Some nonasymptotic results on resampling in high dimension, I: Confidence regions, II: Multiple tests
Sylvain Arlot, Gilles Blanchard, Etienne Roquain
We study generalized bootstrap confidence regions for the mean of a random vector whose coordinates have an unknown dependency structure. The random vector is supposed to be either…
Adaptive FDR control under independence and dependence
Gilles Blanchard, Etienne Roquain
In the context of multiple hypotheses testing, the proportion of true null hypotheses in the pool of hypotheses to test often plays a crucial role, although it is generally u…
Resampling-based confidence regions and multiple tests for a correlated random vector
Sylvain Arlot, Gilles Blanchard, Etienne Roquain
We derive non-asymptotic confidence regions for the mean of a random vector whose coordinates have an unknown dependence structure. The random vector is supposed to be either Gauss…
Occam's hammer: a link between randomized learning and multiple testing FDR control
Gilles Blanchard, François Fleuret
We establish a generic theoretical tool to construct probabilistic bounds for algorithms where the output is a subset of objects from an initial pool of candidates (or more general…
Hierarchical testing designs for pattern recognition
Gilles Blanchard, Donald Geman
We explore the theoretical foundations of a ``twenty questions'' approach to pattern recognition. The object of the analysis is the computational process itself rather than probabi…