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........ published in NEWSLETTER # 52

FROM STATISTICAL PHYSICS TO STATISTICAL INFERENCE AND BACK
by Dr. P. Grassberger and Dr. J._P. Nadal, ENS, Paris (France)

This volume (NATO ASI SERIES C428), following a meeting organised in Cargese (Corsica) from August 31 to September 12, 1992, is about the notion of inference, at the frontier between physics and mathematics. The word `inference' denotes the ability to derive a general rule from a particular set of observations. Physicists, for modeling physical systems with a large degree of freedom, and mathematicians, for performing data analysis, have developped their own concepts and methods for making the `best' inference. Cognitive science is one particular field among others where the notion of inference plays a central role. In particular, both the physical and the mathematical approaches have been used recently in the theory of formal neural networks.

Even if there are well known connections between the various methods (statistical physics is based on the concept of ENTROPY, which is related to the INFORMATION quantity of Shanon), there is a need for clarification. The meeting was a first attempt to detail the possible bridges and gaps between the different approaches.

The book presents the concepts and methods of the main approaches (maximum entropy principle, statistical physics approach to learning: Bayesian approach, minimum description length ...) and present applications (physical systems, neural networks and learning theory, spin_glasses, coding, forecasting time series, ...). After an introductory chapter which gives an idea of the spirit of the meeting, there is a section presenting the main theoretical approaches to inference. Then follows a section on (Shanon) coding and the statistical physics of disordered systems, where the unexpected profound relationship between these two domains is introduced. The next section on learning (mainly neural networks theory) is followed by a section on dynamic systems. Finally, the last section is on the notion of inference in quantum mechanics. There are already volumes on specific topics _ e.g. on learning theory, on maximum entropy principle, etc. _ but there is not a single volume which puts together, in a constructive way, the most relevant approaches to inference theory. This book does exactly that.
Reference books: B135, C428

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