Paper available

[Bert Kappen]

Dear all,
The following paper will be presented at NIPS and is now available
for previewing from my web page. 

Bert Kappen             SNN           University of Nijmegen
tel: +31 24 3614241                      fax: +31 24 3541435
URL: http://www.mbfys.kun.nl/~bert
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Second order approximations for probability models

Bert Kappen, Wim Wiegerinck

In this paper, we derive a second order mean field theory for
directed graphical probability models.
By using an information theoretic argument it is shown how this can be
done
in the absense of a partition function.
This method is the direct generalisation of the
well-known TAP approximation for Boltzmann Machines.
In a numerical example, it is shown that the method greatly improves the
first order mean field approximation.
The computational complexity of the first (second) order method is
linear
(quadratic) in the network size and is
exponential in the potential size. For a restricted class of graphical
models,
so-called single overlap graphs, the second order method has comparable
complexity to the first order method.






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Bert Kappen             SNN           University of Nijmegen
tel: +31 24 3614241                      fax: +31 24 3541435
URL: http://www.mbfys.kun.nl/~bert