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Adaptive Algorithms and Stochastic Approximations

  • Book
  • © 1990

Overview

Authors:
  1. Albert Benveniste

    1. IRISA-INRIA, Rennes Cedex, France

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  2. Michel Métivier
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  3. Pierre Priouret

    1. Laboratoire de Probabilités, Université Pierre et Marie Curie, Paris Cedex, France

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Part of the book series: Stochastic Modelling and Applied Probability (SMAP, volume 22)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xi
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  2. Introduction

    1. Introduction

      • Albert Benveniste, Michel Métivier, Pierre Priouret
      Pages 1-6

  3. Adaptive Algorithms: Applications

    1. Front Matter

      Pages 7-7
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    2. General Adaptive Algorithm Form

      • Albert Benveniste, Michel Métivier, Pierre Priouret
      Pages 9-39

    3. Convergence: the ODE Method

      • Albert Benveniste, Michel Métivier, Pierre Priouret
      Pages 40-102

    4. Rate of Convergence

      • Albert Benveniste, Michel Métivier, Pierre Priouret
      Pages 103-119

    5. Tracking Non-Stationary Parameters

      • Albert Benveniste, Michel Métivier, Pierre Priouret
      Pages 120-164

    6. Sequential Detection; Model Validation

      • Albert Benveniste, Michel Métivier, Pierre Priouret
      Pages 165-198

    7. Appendices to Part I

      • Albert Benveniste, Michel Métivier, Pierre Priouret
      Pages 199-210

  4. Stochastic Approximations: Theory

    1. Front Matter

      Pages 211-211
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    2. O.D.E. and Convergence A.S. for an Algorithm with Locally Bounded Moments

      • Albert Benveniste, Michel Métivier, Pierre Priouret
      Pages 213-250

    3. Application to the Examples of Part I

      • Albert Benveniste, Michel Métivier, Pierre Priouret
      Pages 251-288

    4. Analysis of the Algorithm in the General Case

      • Albert Benveniste, Michel Métivier, Pierre Priouret
      Pages 289-306

    5. Gaussian Approximations to the Algorithms

      • Albert Benveniste, Michel Métivier, Pierre Priouret
      Pages 307-342

    6. Appendix to Part II

      • Albert Benveniste, Michel Métivier, Pierre Priouret
      Pages 343-347

  5. Back Matter

    Pages 349-365
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Keywords

About this book

Adaptive systems are widely encountered in many applications ranging through adaptive filtering and more generally adaptive signal processing, systems identification and adaptive control, to pattern recognition and machine intelligence: adaptation is now recognised as keystone of "intelligence" within computerised systems. These diverse areas echo the classes of models which conveniently describe each corresponding system. Thus although there can hardly be a "general theory of adaptive systems" encompassing both the modelling task and the design of the adaptation procedure, nevertheless, these diverse issues have a major common component: namely the use of adaptive algorithms, also known as stochastic approximations in the mathematical statistics literature, that is to say the adaptation procedure (once all modelling problems have been resolved). The juxtaposition of these two expressions in the title reflects the ambition of the authors to produce a reference work, both for engineers who use these adaptive algorithms and for probabilists or statisticians who would like to study stochastic approximations in terms of problems arising from real applications. Hence the book is organised in two parts, the first one user-oriented, and the second providing the mathematical foundations to support the practice described in the first part. The book covers the topcis of convergence, convergence rate, permanent adaptation and tracking, change detection, and is illustrated by various realistic applications originating from these areas of applications.

Authors and Affiliations

  • IRISA-INRIA, Rennes Cedex, France

    Albert Benveniste

  • Laboratoire de Probabilités, Université Pierre et Marie Curie, Paris Cedex, France

    Pierre Priouret

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