Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!tut.cis.ohio-state.edu!gem.mps.ohio-state.edu!usc!ucla-cs!maui!hector
From: hector@maui.cs.ucla.edu (Hector A Geffner)
Newsgroups: comp.ai.neural-nets
Subject: Re: NN and Bayesian Belief Nets
Message-ID: <29446@shemp.CS.UCLA.EDU>
Date: 22 Nov 89 19:17:43 GMT
References: <1148@uwm.edu> <4454@itivax.iti.org>
Sender: news@CS.UCLA.EDU
Reply-To: hector@cs.ucla.edu (Hector A Geffner)
Organization: UCLA Computer Science Department
Lines: 33

In article <4454@itivax.iti.org> dhw@itivax.UUCP (David H. West) writes:
>In article <1148@uwm.edu> rupen@csd4.csd.uwm.edu (Rupen Dinesh Sheth) writes:
>|I am new in the area of neural nets.  I am trying to compare the neural net
>|approach to the Bayesian Net approach (by Judea Pearl).
>|
>|Has anyone worked on this before?  

See "The Probabilistic Semantics of Connectionist Networks", 
     by Geffner and Pearl, in the Proceedings of the First ICNN, San Diego, 
     1987, pp 187-195

>|                             ....  Is it true that single layer neural nets
>|can perform similar to Bayesian belief networks, and if so has anyone done 
>!some theoretical work on it.

Not as far as i know. Representing Bayesian Networks in connectionist 
architectures requires in general higher order connections (eg w_{i,j,k,....}).

>Typical 'neural net' neurons have an internal state that is
>characterised by a single scalar, and they perform a scalar
>calculation (on which some setups impose the complication of
>back-propagation, in which the links have a scalar state).  Pearl's 
>nodes must store a multi-dimensional matrix, and transmit vector
>messages over their links.
>
>-David West         dhw@itivax.iti.org


For Bayesian Networks involving binary (two-valued) variables only, the vector
messages can be reduced to scalars, and the matrix can be expressed in terms
of weights  and thresholds (see ref above).

-hector