Concentration Inequalities and Model Selection

Ecole d'Eté de Probabilités de Saint-Flour XXXIII - 2003
2007
ISBN: 978-3-540-48497-4
Verlag: Springer Berlin Heidelberg

Buch, Englisch, 343 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 546 g

Reihe: École d'Été de Probabilités de Saint-Flour

Since the impressive works of Talagrand, concentration inequalities have been recognized as fundamental tools in several domains such as geometry of Banach spaces or random combinatorics. They also turn out to be essential tools to develop a non-asymptotic theory in statistics, exactly as the central limit theorem and large deviations are known to play a central part in the asymptotic theory. An overview of a non-asymptotic theory for model selection is given here and some selected applications to variable selection, change points detection and statistical learning are discussed. This volume reflects the content of the course given by P. Massart in St. Flour in 2003. It is mostly self-contained and accessible to graduate students.

Zielgruppe

Research

Autoren/Hrsg.

Massart, Pascal

Picard, Jean

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Technische Wissenschaften Elektronik | Nachrichtentechnik Nachrichten- und Kommunikationstechnik

Inhaltsverzeichnis

Exponential and Information Inequalities.- Gaussian Processes.- Gaussian Model Selection.- Concentration Inequalities.- Maximal Inequalities.- Density Estimation via Model Selection.- Statistical Learning.

Über Autor(innen)

Prof. Massart has received the bronze medal of the CNRS (in mathematics and theoretical physics) in 1988 and the COPPS Presidents’ award in 1998.