TR announcement

[Manfred Opper]

The following papers are now available via anonymous ftp:
(See below for the retrieval procedure)

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    "Bounds for  Predictive Errors in the Statistical Mechanics of Supervised 
     Learning" (Submitted to Physical Review Letters)
     
     M. Opper and D. Haussler
     
     Ref. WUE-ITP-95-019     


     Within a Bayesian framework, by generalizing inequalities 
     known from statistical mechanics, we calculate general upper and 
     lower bounds for a cumulative entropic error, which measures the success 
     in the supervised learning of an unknown rule from examples. 
     Both bounds match asymptotically, when the number m of observed data grows
     large. We find that the information gain from observing a new example 
     decreases universally like d/m. Here d is a dimension that is defined 
     from the scaling of small volumes with respect to a distance in the 
     space of rules.
     (10 pages) 

     AND

     
    "General Bounds on the Mutual Information Between a Parameter and n 
     Conditionally Independent Observations  " 
     
     D. Haussler and M. Opper: (Proceedings of the 8th Ann. Conf. on
     Computational Learning Theory: COLT 95)

     Ref . WUE-ITP-95-020 

     Each parameter theta in an abstract parameter space Theta is associated
     with a different probability distribution on a set Y. A parameter
     w is chosen at random from Theta according to some a priori
     distribution on theta, and n conditionally independent random variables
     Y^n = Y_1,..., Y_n are observed with common distribution determined 
     by theta. We obtain bounds on the mutual information between the random
     variable theta, giving the choice of parameter, and the 
     random variable Y^n, giving the sequence of observations. We also
     bound the supremum of the mutual information, over choices of the prior
     distribution on Theta.
     These quantities have applications in density estimation, 
     computational learning theory, universal coding, hypothesis testing, 
     and portfolio selection theory.
     The bounds are given in terms of the metric and information
     dimensions of the parameter space Theta with respect to the 
     Hellinger distance.
     (11 pages)



     Manfred Opper
     
     present adress: The Baskin Center for Computer Engineering &
     Information Sciences, University of California
     Santa Cruz CA 95064
      
     email: opper at cse.ucsc.edu

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Retrieval procedure:

     unix> ftp  ftp.physik.uni-wuerzburg.de
     Name: anonymous  Password: {your e-mail address}
     ftp>  cd pub/preprint
     ftp>  get WUE-ITP-95-0??.ps.gz           (*)   
     ftp>  quit
     unix> gunzip WUE-ITP-95-0??.ps.gz
e.g. unix> lp WUE-ITP-95-0??.ps               (7 pages of output)

(*) can be replaced by "get WUE-ITP-95-0??.ps". The file will then
    be uncompressed before transmission (slower!). 
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