Practical computation time needed to perform approximate inferences with a trained Bayesian network.

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I have a task of estimating probabilities of events occurring for which a Bayesian Network appears to be an excellent modelling choice. Ample data and computational time will be available for training. The estimates can be fairly rough approximations. From what I've been reading, the simplest modelling formalisms will suffice for my task.

However, I need to perform inferences in real-time, i.e. time from inputs defining the values of some nodes in the network, to finishing calculation of probabilities represented by some other nodes, (approximately, and using the trained network), needs to be below 100 milliseconds on a decent PC.

Network size will be around 100 nodes, with most nodes only having 3-5 parents.

Is this at all realistic? What approximation algorithms should I be looking at? Can you recommend any tools/libraries (open source preferred)?

Note: I've done a lot of work with neural networks, but know relatively little technically about Bayesian Networks...

Thanks!