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We prove a new and general concentration inequality for the excess risk inleast-squares regression with random design and heteroscedastic noise. Nospecific structure is required on the model, except the existence of a suitablefunction that controls the local suprema of the empirical process. So far, onlythe case of linear contrast estimation was tackled in the literature with thislevel of generality on the model. We solve here the case of a quadraticcontrast, by separating the behavior of a linearized empirical process and theempirical process driven by the squares of functions of models.

A concentration inequality for the excess risk in least-squares regression with random design and heteroscedastic noise