Buch, Englisch, 284 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 446 g
Ecole d'Eté de Probabilités de Saint-Flour XXXI - 2001
Buch, Englisch, 284 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 446 g
Reihe: École d'Été de Probabilités de Saint-Flour
ISBN: 978-3-540-22572-0
Verlag: Springer Berlin Heidelberg
Statistical learning theory is aimed at analyzing complex data with necessarily approximate models. This book is intended for an audience with a graduate background in probability theory and statistics. It will be useful to any reader wondering why it may be a good idea, to use as is often done in practice a notoriously "wrong'' (i.e. over-simplified) model to predict, estimate or classify. This point of view takes its roots in three fields: information theory, statistical mechanics, and PAC-Bayesian theorems. Results on the large deviations of trajectories of Markov chains with rare transitions are also included. They are meant to provide a better understanding of stochastic optimization algorithms of common use in computing estimators. The author focuses on non-asymptotic bounds of the statistical risk, allowing one to choose adaptively between rich and structured families of models and corresponding estimators. Two mathematical objects pervade the book: entropy and Gibbs measures. The goal is to show how to turn them into versatile and efficient technical tools, that will stimulate further studies and results.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz Wissensbasierte Systeme, Expertensysteme
- Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
- Mathematik | Informatik Mathematik Operations Research Spieltheorie
- Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
Weitere Infos & Material
Universal Lossless Data Compression.- Links Between Data Compression and Statistical Estimation.- Non Cumulated Mean Risk.- Gibbs Estimators.- Randomized Estimators and Empirical Complexity.- Deviation Inequalities.- Markov Chains with Exponential Transitions.- References.- Index.
