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Statistical learning theory and stochastic optimization. Ecole d’Eté de Probabilitiés de Saint-Flour XXXI – 2001. (English) Zbl 1076.93002
Lecture Notes in Mathematics 1851. Berlin: Springer (ISBN 3-540-22572-2/pbk). viii, 273 p. (2004).
The main topic of the book is to estimate a probability distribution from observed samples. A risk function of the Kullback divergence type is considered. Other types of risk functions are also considered. Oracle inequalities are associated to estimators restricted to a (possibly random) parametrization. The goal is to bound the unresticted risk by the restricted one plus a term quantifying the complexity of the parametric model. The first chapters give connections with coding theory, universal lossless data compression, and pattern recognition. Then several types of oracle inequalities are studied. Finally, some connections with simulated annealing are investigated.
90 references and an index are provided at the end.
This book is an advanced study and accessibility to a broader readership could be improved.

MSC:
93-02 Research exposition (monographs, survey articles) pertaining to systems and control theory
93E10 Estimation and detection in stochastic control theory
93E24 Least squares and related methods for stochastic control systems
93E35 Stochastic learning and adaptive control
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
62B10 Statistical aspects of information-theoretic topics
62G99 Nonparametric inference
62M05 Markov processes: estimation; hidden Markov models
68T10 Pattern recognition, speech recognition
90C15 Stochastic programming
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