PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Functional classification with margin conditions
Magalie Fromont and Christine Tuleau
Lecture Notes in Computer Science Volume 4005, pp. 94-108, 2006. ISSN 0302-9743

Abstract

Let (X,Y) be a X×{0,1} valued random pair and consider a sample (X1,Y1),...,(Xn,Yn) drawn from the distribution of (X,Y). We aim at constructing from this sample a classifier that is a function which would predict the value of Y from the observation of X. The special case where is a functional space is of particular interest due to the so called curse of dimensionality. In a recent paper, Biau et al. propose to filter the Xi’s in the Fourier basis and to apply the classical k–Nearest Neighbor rule to the first d coefficients of the expansion. The selection of both k and d is made automatically via a penalized criterion. We extend this study, and note here the penalty used by Biau et al. is too heavy when we consider the minimax point of view under some margin type assumptions. We prove that using a penalty of smaller order or equal to zero is preferable both in theory and practice. Our experimental study furthermore shows that the introduction of a small-order penalty stabilizes the selection process, while preserving rather good performances.

EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
ID Code:2874
Deposited By:Magalie Fromont
Deposited On:22 November 2006