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Concentration Inequalities and Model Selection

Ecole d'Eté de Probabilités de Saint-Flour XXXIII - 2003

Pascal Massart (Autor)

Jean Picard (Herausgeber)

Buch | Softcover

XIV, 343 Seiten

2007
Springer Berlin (Verlag)
978-3-540-48497-4 (ISBN)

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Concentration inequalities have been recognized as fundamental tools in several domains such as geometry of Banach spaces or random combinatorics. They also turn to be essential tools to develop a non asymptotic theory in statistics. This volume provides an overview of a non asymptotic theory for model selection. It also discusses some selected applications to variable selection, change points detection and statistical learning.

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.

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

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

Erscheint lt. Verlag	18.4.2007
Reihe/Serie	École d'Été de Probabilités de Saint-Flour
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	XIV, 343 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	551 g
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	60C05; 60E15; 60F10; 62B10; 62E17; 62G05; 62G07; 62G08; 62J0 • 62J0 • adaptive estimation • concentration inequalities • empirical processes • Information • Information and Communication, Circuits • Maxima • Model Selection • Statistical Learning
ISBN-10	3-540-48497-3 / 3540484973
ISBN-13	978-3-540-48497-4 / 9783540484974
Zustand	Neuware