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I have used the Bayes Net Toolbox to build a small network, which consists of 3 nodes and is shown below.

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Node 1 is a Bernoulli random variable, node 2 is a Gaussian random variable and node 3 is a softmax random variable with 3 possible values. The data is incomplete, so I use the EM algorithm to estimate the parameters. But the log-likelihood decreases from the beginning and stops with the last two iterations being equal.

Does anyone know the possible solution to this situation?

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If you included a prior distribution, then an EM algorithm would converge to the mode of the posterior distribution. In such a case, the log likelihood may decrease, but the combined term of (log likelihood + log prior) would increase at every iteration.

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