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From Statistical Physics to Statistical Inference and Back

  • Book
  • © 1994

Overview

Editors:
  1. Peter Grassberger

    1. Department of Theoretical Physics, University of Wuppertal, Wuppertal, Germany

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    You can also search for this editor in PubMed   Google Scholar

  2. Jean-Pierre Nadal

    1. Laboratory of Statistical Physics, École Normale Supérieure, Paris, France

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Nato Science Series C: (ASIC, volume 428)

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Table of contents (23 chapters)

  1. Front Matter

    Pages i-viii
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  2. In place of an Introduction

    1. Concluding Remarks

      • Gérard Toulouse
      Pages 1-9

  3. Principles for Inference

    1. Statistical Mechanics and the Maximum Entropy Method

      • Roger Balian
      Pages 11-43

    2. Irreversibility, Probability and Entropy

      • Anthony J. M. Garrett
      Pages 45-75

    3. Maximum Entropy for Random Cellular Structures

      • Nicolas Rivier
      Pages 77-93

    4. MDL Modeling — An Introduction

      • Jorma Rissanen
      Pages 95-104

    5. An Introduction to Learning and Generalisation

      • Giorgio Parisi
      Pages 105-112

    6. Information Geometry and Manifolds of Neural Networks

      • Shun-ichi Amari
      Pages 113-138

    7. Uncertainty as a Resource for Managing Complexity

      • George J. Klir
      Pages 139-153

  4. Coding and Statistical Physics of Disordered Systems

    1. The Development of Information Theory

      • Sergio Verdu
      Pages 155-167

    2. Statistical Inference, Zero Knowledge and Proofs of Identity

      • Jacques Stern
      Pages 169-182

    3. Spin Glasses: An Introduction

      • Marc Mézard
      Pages 183-193

    4. Statistical Mechanics and Error-Correcting Codes

      • Nicolas Sourlas
      Pages 195-204

  5. Learning

    1. Learning and Generalization with Undetermined Architecture

      • Naftali Tishby
      Pages 205-224

    2. Confronting Neural Network and Human Behavior in a Quasiregular Environment

      • Miguel A. Virasoro
      Pages 225-235

    3. Sensory Processing and Information Theory

      • Ralph Linsker
      Pages 237-247

    4. The Formation of Representations in the Visual Cortex

      • H.-U. Bauer, T. Geisel, K. Pawelzik, F. Wolf
      Pages 249-261

    5. Classifier Systems: Models for Learning Agents

      • David A. Lane
      Pages 263-280

  6. Dynamical Systems

    1. Space Time Dynamics and Biorthogonal Analysis Mementum

      • Ricardo Lima
      Pages 281-291

    2. Symbolic Encoding in Dynamical Systems

      • Antonio Politi
      Pages 293-309
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Keywords

About this book

Physicists, when modelling physical systems with a large number of degrees of freedom, and statisticians, when performing data analysis, have developed their own concepts and methods for making the `best' inference. But are these methods equivalent, or not? What is the state of the art in making inferences? The physicists want answers. More: neural computation demands a clearer understanding of how neural systems make inferences; the theory of chaotic nonlinear systems as applied to time series analysis could profit from the experience already booked by the statisticians; and finally, there is a long-standing conjecture that some of the puzzles of quantum mechanics are due to our incomplete understanding of how we make inferences. Matter enough to stimulate the writing of such a book as the present one.
But other considerations also arise, such as the maximum entropy method and Bayesian inference, information theory and the minimum description length. Finally, it is pointed out that an understanding of human inference may require input from psychologists. This lively debate, which is of acute current interest, is well summarized in the present work.

Editors and Affiliations

  • Department of Theoretical Physics, University of Wuppertal, Wuppertal, Germany

    Peter Grassberger

  • Laboratory of Statistical Physics, École Normale Supérieure, Paris, France

    Jean-Pierre Nadal

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