An efficient Averaged Stochastic Gauss-Newton algorithm for estimating parameters of non linear regressions models

Peggy Cénac (1) , Antoine Godichon-Baggioni (2) , Bruno Portier (3)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation
3 LMI - Laboratoire de Mathématiques de l'INSA de Rouen Normandie

Non linear regression models are a standard tool for modeling real phenomena, with several applications in machine learning, ecology, econometry... Estimating the parameters of the model has garnered a lot of attention during many years. We focus here on a recursive method for estimating parameters of non linear regressions. Indeed, these kinds of methods, whose most famous are probably the stochastic gradient algorithm and its averaged version, enable to deal efficiently with massive data arriving sequentially. Nevertheless, they can be, in practice, very sensitive to the case where the eigen-values of the Hessian of the functional we would like to minimize are at different scales. To avoid this problem, we first introduce an online Stochastic Gauss-Newton algorithm. In order to improve the estimates behavior in case of bad initialization, we also introduce a new Averaged Stochastic Gauss-Newton algorithm and prove its asymptotic efficiency.

Domaines: Théorie [stat.TH]

Peggy Cénac, Antoine Godichon-Baggioni, Bruno Portier. An efficient Averaged Stochastic Gauss-Newton algorithm for estimating parameters of non linear regressions models. 2020. ⟨hal-02876141v2⟩