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
Year: 2023
Type: preprint
Abstract: 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 large probability for four estimators: ERM, minmax MOM and their regularized versions. These general bounds are applied for the problem of robustness in sparse PCA. In particular, we improve the state of the art result for this this problems, obtain results under weak moment assumptions as well as for adversarial contaminated data.
Source: arXiv (Cornell University)
Authors: Lecué, Guillaume, Neirac, Lucie
Institutions: Centre de Recherche en Économie et Statistique, ENSAE Paris
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4387995294