7 papers
Sharp convergence rate of the estimation error of LASSO via the Feature Space Decomposition method
Guillaume Lecué, Zong Shang
In this paper, we use the Feature Space Decomposition (FSD) method to establish an explicit, non-asymptotic, instance-optimal convergence rate for the estimation error of the LASSO…
Benign Overfitting Property of the Minimum -norm Interpolant Estimator in Regression Problem via Feature Space Decomposition
Radosław Adamczak, Guillaume Lecué, Zong Shang +1
This paper establishes high-probability, non-asymptotic upper bounds for the population excess risk of minimum -norm interpolating estimators in linear regression, valid fo…
The Geometry of Statistical Feature Learning in Mean-Field Langevin Dynamics
Zong Shang, Tomoya Wakayama, Guillaume Lecué +1
We introduce a geometric formulation of statistical feature learning for supervised regression. Feature learning is defined through a base--fiber decomposition: the base is the fea…
Sharp convergence rates for Spectral methods via the feature space decomposition method
Guillaume Lecué, Zhifan Li, Zong Shang
In this paper, we apply the Feature Space Decomposition (FSD) method developed in [LS24, GLS25, LSSW26, ALSS26] to obtain, under fairly general conditions, matching upper and lower…
Upper bounds for the L^q empirical process via generic chaining
Zong Shang
Using the generic chaining method, we derive upper bounds for the \(L^q\) process of sub-Gaussian classes when \(1 \le q \le 2\), thereby resolving an open problem posed by Al-Ghat…
A Geometrical Analysis of Kernel Ridge Regression and its Applications
Georgios Gavrilopoulos, Guillaume Lecué, Zong Shang
We obtain upper bounds for the estimation error of Kernel Ridge Regression (KRR) for all non-negative regularization parameters, offering a geometric perspective on various phenome…
A geometrical viewpoint on the benign overfitting property of the minimum -norm interpolant estimator and its universality
Guillaume Lecué, Zong Shang
In the linear regression model, the minimum l2-norm interpolant estimator has received much attention since it was proved to be consistent even though it fits noisy data perfectly…