2011/02/14 by Yannick Baraud, Baraud, Yannick, Lucien Birgé +1 · 1 citation
Computer Science · Mathematics · #62G05 #Bayesian Methods and Mixture Models #FOS: Mathematics #Machine Learning and Algorithms #Rough Sets and Fuzzy Logic #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #msc:62G05 #stat.TH
paper · pdf · doi:10.48550/arxiv.1102.2818
37 pages
openalex publication_date 2011/02/14 · arxiv created 2013/01/27 · arxiv updated 2013/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the problem of estimating a function s on [-1,1]k for large values of k by looking for some best approximation by composite functions of the form g∘ u. Our solution is based on model selection and leads to a very general approach to solve this problem with respect to many different types of functions g,u and statistical frameworks. In particular, we handle the problems of approximating s by additive functions, single and multiple index models, neural networks, mixtures of Gaussian densities (when s is a density) among other examples. We also investigate the situation where s=g∘ u for functions g and u belonging to possibly anisotropic smoothness classes. In this case, our approach leads to a completely adaptive estimator with respect to the regularity of s.