4 papers · 1 filter
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…
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…
Learning with a linear loss function. Excess risk and estimation bounds for ERM, minmax MOM and their regularized versions. Applications to robustness in sparse PCA
Guillaume Lecué, Lucie Neirac
Motivated by several examples, we consider a general framework of learning with linear loss functions. In this context, we provide excess risk and estimation bounds that hold with…