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PRL
2011

Consistency of functional learning methods based on derivatives

8 years 1 months ago
Consistency of functional learning methods based on derivatives
In some real world applications, such as spectrometry, functional models achieve better predictive performances if they work on the derivatives of order m of their inputs rather than on the original functions. As a consequence, the use of derivatives is a common practice in functional data analysis, despite a lack of theoretical guarantees on the asymptotically achievable performances of a derivative based model. In this paper, we show that a smoothing spline approach can be used to preprocess multivariate observations obtained by sampling functions on a discrete and finite sampling grid in a way that leads to a consistent scheme on the original infinite dimensional functional problem. This work extends Mas and Pumo (2009) to nonparametric approaches and incomplete knowledge. To be more precise, the paper tackles two difficulties in a nonparametric framework: the information loss due to the use of the derivatives instead of the original functions and the information loss due to the ...
Fabrice Rossi, Nathalie Villa-Vialaneix
Added 14 May 2011
Updated 14 May 2011
Type Journal
Year 2011
Where PRL
Authors Fabrice Rossi, Nathalie Villa-Vialaneix
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