2017/02/16 by Adrien Saumard, Saumard, Adrien
Environmental Science · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Point processes and geometric inequalities #Soil Geostatistics and Mapping #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1702.05063
openalex publication_date 2017/02/16 · openalex created_date 2017/04/28 · openalex updated_date 2026/07/28
We prove a new and general concentration inequality for the excess risk in least-squares regression with random design and heteroscedastic noise. No specific structure is required on the model, except the existence of a suitable function that controls the local suprema of the empirical process. So far, only the case of linear contrast estimation was tackled in the literature with this level of generality on the model. We solve here the case of a quadratic contrast, by separating the behavior of a linearized empirical process and the empirical process driven by the squares of functions of models.