42 citations · 68 across the 7 of their papers we have counts for
8 papers
Optimal minimization of an unknown function in a nonparametric multivariate regression model thanks to a dimension reduction approach
Cédric Adam, Ilaria Giulini, Céline Lévy-Leduc
In this paper, we propose a novel approach for estimating the minimum of a smooth function and its location from observations corresponding to a multivariate regression function de…
Dimension-free PAC-Bayesian bounds for the estimation of the mean of a random vector
Olivier Catoni, Ilaria Giulini
In this paper, we present a new estimator of the mean of a random vector, computed by applying some threshold function to the norm. Non asymptotic dimension-free almost sub-Gaussia…
Dimension-free PAC-Bayesian bounds for matrices, vectors, and linear least squares regression
Olivier Catoni, Ilaria Giulini
This paper is focused on dimension-free PAC-Bayesian bounds, under weak polynomial moment assumptions, allowing for heavy tailed sample distributions. It covers the estimation of t…
Data driven estimation of Laplace-Beltrami operator
Frédéric Chazal, Ilaria Giulini, Bertrand Michel
Approximations of Laplace-Beltrami operators on manifolds through graph Lapla-cians have become popular tools in data analysis and machine learning. These discretized operators usu…
Kernel Spectral Clustering
Ilaria Giulini
We investigate the question of studying spectral clustering in a Hilbert space where the set of points to cluster are drawn i.i.d. according to an unknown probability distribution…
Robust Principal Component Analysis in Hilbert spaces
Ilaria Giulini
We propose a stable version of Principal Component Analysis (PCA) in the general framework of a separable Hilbert space. It consists in interpreting the projection on the first eig…
PAC-Bayesian bounds for Principal Component Analysis in Hilbert spaces
Ilaria Giulini
Based on some new robust estimators of the covariance matrix, we propose stable versions of Principal Component Analysis (PCA) and we qualify it independently of the dimension of t…
Robust dimension-free Gram operator estimates
Ilaria Giulini
In this paper we investigate the question of estimating the Gram operator by a robust estimator from an i.i.d. sample in a separable Hilbert space and we present uniform bounds tha…