Informatique Pr Esent Ee Par : Statistical Learning and Regularisation for Regression Application to System Identiication and Time Series Modelling Apprentissage Statistique Et Regularisation Pour La R Egression

Application a l'identiication de syst emes et a la mod elisation des s eries chronologiques soutenue le 7 juillet 1997 devant le jury compos e de : Acknowledgements i Acknowledgements I am indebted to Professor Patrick Gallinari, who took me under his supervision in 1992, and followed me throughout this work. I would like him to know that his friendly support during these years were largely instrumental in the completion of this thesis. I would also like to thank Professor Lars Kai Hansen for welcoming me at the now-defunct Electronics Institute during the year 1995-1996, and later at the Institute of Mathematical Modelling. His enthusiastic comments and support had a major innuence on my work. I wish to express my gratitude to the members of the jury, who undertook to evaluate my work. Sylvie Thiria accepted to be the head of this jury; Anne Gu erin-Dugu e and G erard Govaert reviewed and refereed this thesis; Jan Larsen showed great interest in my work and accepted to y from Denmark to be part of this jury. I also wish to express my gratitude to all those who helped me through many fruitful discussions, or just by creating a friendly and challenging working atmosphere. The PhD students or ex-PhD students of the connectionist group of Laforia (Paris 6 University), and of the Digital Signal Processing group (Technical University of Denmark). Finally, special thanks are in order for my wife Kia. I don't know what I should thank her more for: her continued support and exaltation, or just putting up with me while I was writing this manuscript. I am especially indebted to those who provided advices, software and other gimmicks that helped the completion of this thesis. I owe Peter Toft as I borrowed some of his L A T E X style, and his si.m matlab visualisation function among other things. L A T E X also got me indebted to Peter S.K. Hansen and Jan Larsen. I am also pleased to thank Xavier Driancourt and Neuristique S.A. for lending me a version of the TLisp/SN software while I was away, and taking care of my endless requests on top of it. This document was written using a customised version of the L A T E X book format with packages fancyhdr, graphicx, apalike and makeidx. Introduction Notation Here are a number of symbols that are used throughout the text, …