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I am working on a problem where every node in the Bayesian network is continuous random variable and the structure of the network is known. This network comprises of both observed and latent nodes, and each node has physical significance (can be observed using experiments). For simplicity I am assuming a linear gaussian CPD for all the nodes, and I am interested in estimating the parameters in this model.

I have come across the literature where EM algorithm is used to estimate the parameters in the latent and observed variables, but only for a special cases like the probabilistic PCA, factor analysis etc. where the purpose is dimension reduction so the latent variable is connected to all observed variables in the model. I would like to estimate the latent variable parameters (and hence the distributions) for a more general network case.

It would be great if anyone can point me to literature/examples which deal with inference/estimation in a more general Bayesian networks with continuous latent and observed nodes.

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  • $\begingroup$ Any Kalman filter or other continuous state estimation scheme has continuous latent and observed nodes. // Also check out the tutorials / example pages for probabilistic inference packages such as pyro, stan, etc. There you'll find loads of standard and more complex examples. $\endgroup$
    – Eike P.
    Commented Oct 24, 2023 at 10:29

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If you're looking on literature on methods for approximating latent/hidden variables in Bayesian Networks, I suggest reading:

  1. Efficent Approximations for the Marginal Likelihood of Bayesian Networks with HiddenVariables

  2. A Tutorial on Learning With Bayesian Networks

They're not the easiest reads, so I recommend also looking at what other papers they reference.

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