| Description : |
In this talk, we deal with the problem of density estimation. We aim at building an estimate of an unknown density as a linear combination of functions of a dictionary. Inspired by Cand\`es and Tao's approach, we propose a $\ell_1$-minimization under an adaptive Dantzig constraint coming from sharp concentration inequalities. This allows to consider a wide class of
dictionaries. Under coherence assumptions, oracle inequalities are derived. These theoretical results are also proved to be valid for the natural Lasso estimate associated with our Dantzig procedure. Then, the issue of calibrating these procedures is studied from both theoretical and practical points of view. Finally, a numerical study shows the significant improvement obtained by our procedures when compared with other classical procedures. |
| Equipe organisatrice : |
Probabilités et Statistiques |
| Jury (Thèse / HDR) : |
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| Orateur : |
Vincent Rivoirard |
| Titre (Thèse / HDR) : |
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| Université Orateur : |
Paris Sud-Orsay |
| URL Orateur : |
http://www.math.u-psud.fr/~rivoirar/ |
| Ressource : |
Laboratoire J.A.Dieudonné - Salle de conférence |
| Date de début : |
11:30 - jeudi 07 janvier 2010 |
| Durée : |
1 heure(s) |
| Date de fin : |
12:30 - jeudi 07 janvier 2010 |
| Type : |
Séminaire |
| Réservation effectuée par : |
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| Dernière mise à jour : |
14:10 - lundi 16 novembre 2009 |