Paper: A priori information, statistical mechanics

[Joerg_Lemm]

The following technical report is available at:     
                 http://pauli.uni-muenster.de/~lemm
or directly: 
                 http://pauli.uni-muenster.de/~lemm/papers/ann98.ps.gz
or at the Los Alamos preprint server as cond-mat/9808039 (gzipped ps-file):
                 http://xxx.lanl.gov/ps/cond-mat/9808039


Joerg C. Lemm:

"How to Implement A Priori Information:
 A Statistical Mechanics Approach"

 Generalization abilities of empirical learning systems are essentially 
 based on a priori information. The paper emphasizes the need of empirical 
 measurement of a priori information by a posteriori control.
 A priori information is treated analogously to an infinite number of training 
 data and expressed explicitly in terms of the function values of interest.
 This contrasts an implicit implementation of a priori information,
 e.g., by choosing a restrictive function parameterization.
 Different possibilities to implement a priori information are presented.
 Technically, the proposed methods are non--convex (non--Gaussian) extensions 
 of classical quadratic and thus convex regularization approaches
 (or Gaussian processes, respectively). Specific topics discussed include
 approximate symmetries, approximate structural assumptions, 
 transfer of knowledge and combination of learning systems.
 Appendix A compares concepts of statistics and statistical mechanics.
 Appendix B relates the paper to the framework of Bayesian decision theory.

University of Muenster Publication No.: MS-TP1-98-12

Available at:     
                 http://pauli.uni-muenster.de/~lemm
or directly: 
                 http://pauli.uni-muenster.de/~lemm/papers/ann98.ps.gz
or at the Los Alamos preprint server as cond-mat/9808039 (gzipped ps-file):
                 http://xxx.lanl.gov/ps/cond-mat/9808039


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Dr. Joerg Lemm                      
Universitaet Muenster                        Email: lemm at uni-muenster.de     
Institut fuer Theoretische Physik I          Phone:     +49(251)83-34922
Wilhelm-Klemm-Str.9                            Fax:     +49(251)83-36328
D-48149 Muenster, Germany             http://pauli.uni-muenster.de/~lemm      
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