Adaptive sequential design for regression on multi-resolution bases

Serge Cohen (1) , Sébastien Dejean (1) , Sébastien Gadat (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

This work investigates the problem of construction of designs for estimation and discrimination between competing linear models. In our framework, the unknown signal is observed with the addition of a noise and only a few evaluations of the noisy signal are available. The model selection is performed in a multi-resolution setting. In this setting, the locations of discrete sequential D and A designs are precisely constraint in a small number of explicit points. Hence, an efficient stochastic algorithm can be constructed that alternately improves the design and the model. Several numerical experiments illustrate the efficiency of our method for regression. One can also use this algorithm as a preliminary step to build response surfaces for sensitivity analysis.

Mots clés: Active learning; Optimal designs; Stochastic algorithms; Model selection; Wavelets

Domaines: Théorie [stat.TH]

Serge Cohen, Sébastien Dejean, Sébastien Gadat. Adaptive sequential design for regression on multi-resolution bases. Statistics and Computing, 2012, 22 (3), pp.753-772. ⟨10.1007/s11222-011-9267-7⟩. ⟨hal-00714865⟩