I've tried 2 approaches for inference and learning in real-valued
belief nets, where P(child|parents) is a nonlinear function (eg, sigmoid)
applied to a Gaussian random variable with mean equal to a weighted
sum of the parent values.

The first is "slice sampling",

B. J. Frey 1997. Continuous sigmoidal belief networks
     trained using slice sampling. In Advances in Neural
     Information Processing Systems 9. MIT Press:
     Cambridge, MA.

The second is a variational technique for inference and learning,

B. J. Frey and G. E. Hinton 1999. Variational learning in
     nonlinear Gaussian belief networks. Neural Computation
     11:1, 193-214.

Both papers are available at www.cs.uwaterloo.ca/~frey

Brendan.

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Brendan J. Frey       [EMAIL PROTECTED]       www.cs.toronto.edu/~frey
Tel: +1 519 888 4567 ext 6242                     Fax: +1 519 885 1208 

Interests: Adaptive computation in computers and neural networks;
probabilistic and statistical inference in complex systems for vision,
digital communication, machine learning, signal processing and data
compression.

Assistant Professor, Computer Science, University of Waterloo, Davis
    Centre, Waterloo, Ontario, CANADA N2L 3G1

Adjunct Assistant Professor, Elec. and Comp. Eng., Univ. of Illinois

Visiting Professor, Beckman Institute for Advanced Science and Tech.
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