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math.ST2026
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…
math.ST2026
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…
math.ST2024
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…