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Functional multi-layer perceptron: A nonlinear tool for functional data analysis. (English) Zbl 1085.68134
Summary: We study a natural extension of Multi-Layer Perceptrons (MLP) to functional inputs. We show that fundamental results for classical MLP can be extended to functional MLP. We obtain universal approximation results that show the expressive power of functional MLP is comparable to that of numerical MLP. We obtain consistency results, which imply that the estimation of optimal parameters for functional MLP is statistically well defined. We finally show on simulated and real world data that the proposed model performs in a very satisfactory way.

MSC:
68T05 Learning and adaptive systems in artificial intelligence
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