10 citations · 20 across the 19 of their papers we have counts for
23 papers
Pointwise convergence of purely random partition estimators: from random trees to prototype rules
Jérémy Bettinger, François Portier, Adrien Saumard
We study pointwise convergence rates of purely random partition estimators in nonparametric regression, where the partition -- into hyper-rectangles by purely random trees, or into…
Revisiting local regression: shape regularity, uniform rates, and the limits of random splits
Jérémy Bettinger, François Portier, Adrien Saumard
Considering pointwise and sup-norm estimation, we analyze the non-asymptotic behavior of local averaging estimators for Lipschitz regression functions. Building on a general deviat…
Concentration of the bootstrap empirical process, with applications to statistical inference
Guillaume Maillard, Adrien Saumard
Considering a general framework of bootstrap with exchangeable weights, we show some concentration inequalities for the supremum of the bootstrap empirical process. On the one hand…
On the pointwise and sup-norm errors for local regression estimators
Jérémy Bettinger, François Portier, Adrien Saumard
In this paper, we analyze the behavior of various non-parametric local regression estimators, i.e. estimators that are based on local averaging, for estimating a Lipschitz regressi…
A theory of shape regularity for local regression maps
Jérémy Bettinger, François Portier, Adrien Saumard
We introduce the concept of shape-regular regression maps as a framework to derive optimal rates of convergence for various non-parametric local regression estimators. Using Vapnik…
Covariance inequalities for convex and log-concave functions
Michel Bonnefont, Erwan Hillion, Adrien Saumard
Extending results of Harg{é} and Hu for the Gaussian measure, we prove inequalities for the covariance Cov where is a general product probability measure on $\mathbb{…
High-dimensional logistic entropy clustering
Edouard Genetay, Adrien Saumard, Rémi Coulaud
Minimization of the (regularized) entropy of classification probabilities is a versatile class of discriminative clustering methods. The classification probabilities are usually de…
Phase transitions for support recovery under local differential privacy
Cristina Butucea, Amandine Dubois, Adrien Saumard
We address the problem of variable selection in a high-dimensional but sparse mean model, under the additional constraint that only privatised data are available for inference. The…
Relaxing the Gaussian assumption in Shrinkage and SURE in high dimension
Max Fathi, Larry Goldstein, Gesine Reinert +1
Shrinkage estimation is a fundamental tool of modern statistics, pioneered by Charles Stein upon his discovery of the famous paradox involving the multivariate Gaussian. A large po…
K-bMOM: a robust Lloyd-type clustering algorithm based on bootstrap Median-of-Means
Camille Brunet-Saumard, Edouard Genetay, Adrien Saumard
We propose a new clustering algorithm that is robust to the presence of outliers in the dataset. We perform Lloyd-type iterations with robust estimates of the centroids. More preci…
Bi-log-concavity: some properties and some remarks towards a multi-dimensional extension
Adrien Saumard
Bi-log-concavity of probability measures is a univariate extension of the notion of log-concavity that has been recently proposed in a statistical literature. Among other things, i…
Local differential privacy: Elbow effect in optimal density estimation and adaptation over Besov ellipsoids
Cristina Butucea, Amandine Dubois, Martin Kroll +1
We address the problem of non-parametric density estimation under the additional constraint that only privatised data are allowed to be published and available for inference. For t…
An extremal property of the normal distribution, with a discrete analog
Erwan Hillion, Oliver Johnson, Adrien Saumard
We prove, using the Brascamp-Lieb inequality, that the Gaussian measure is the only strong log-concave measure having a strong log-concavity parameter equal to its covariance matri…
Weighted Poincaré inequalities, concentration inequalities and tail bounds related to the Stein kernels in dimension one
Adrien Saumard
We investigate links between the so-called Stein's density approach in dimension one and some functional and concentration inequalities. We show that measures having a finite first…
Finite sample improvement of Akaike's Information Criterion
Adrien Saumard, Fabien Navarro
We emphasize that it is possible to improve the principle of unbiased risk estimation for model selection by addressing excess risk deviations in the design of penalization procedu…
On the isoperimetric constant, covariance inequalities and -Poincaré inequalities in dimension one
Adrien Saumard, Jon A. Wellner
Firstly, we derive in dimension one a new covariance inequality of type that characterizes the isoperimetric constant as the best constant achieving the inequali…
Efron's monotonicity property for measures on
Adrien Saumard, Jon A. Wellner
First we prove some kernel representations for the covariance of two functions taken on the same random variable and deduce kernel representations for some functionals of a continu…
A concentration inequality for the excess risk in least-squares regression with random design and heteroscedastic noise
Adrien Saumard
We prove a new and general concentration inequality for the excess risk in least-squares regression with random design and heteroscedastic noise. No specific structure is required…
On optimality of empirical risk minimization in linear aggregation
Adrien Saumard
In the first part of this paper, we show that the small-ball condition, recently introduced by Mendelson (2015), may behave poorly for important classes of localized functions such…
Slope heuristics and V-Fold model selection in heteroscedastic regression using strongly localized bases
Fabien Navarro, Adrien Saumard
We investigate the optimality for model selection of the so-called slope heuristics, -fold cross-validation and -fold penalization in a heteroscedastic with random design reg…
Log-concavity and strong log-concavity: a review
Adrien Saumard, Jon A. Wellner
We review and formulate results concerning log-concavity and strong-log-concavity in both discrete and continuous settings. We show how preservation of log-concavity and strongly l…
Optimal upper and lower bounds for the true and empirical excess risks in heteroscedastic least-squares regression
Adrien Saumard
We consider the estimation of a bounded regression function with nonparametric heteroscedastic noise and random design. We study the true and empirical excess risks of the least-sq…
The Slope Heuristics in Heteroscedastic Regression
Adrien Saumard
We consider the estimation of a regression function with random design and heteroscedastic noise in a nonparametric setting. More precisely, we address the problem of characterizin…