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Updating rules for the parameter estimates. Calculation of the expectations in the MTE framework. The EM algorithm will be used to find maximum likelihood parameter estimates for the distributions involved. Since we need to make inference in the EM algorithm and we cannot do this exactly in a general hybrid Bayesian network, the current distributions will be translated into MTEs in each iteration in order to make the inference feasible.
So, we will be working in parallel with an MTE network for doing inference and the original network. A fixed graph structure for B. Output: A Bayesian network B. For this transformation we can use the procedures in [1, 2]. This inference process will be made using the existing implementation in Elvira. B 7 until convergence ; 8 return B. Updating rules for the parameter estimates In this section we will get the updating rules for the different distributions under consid- eration.
We will assume a Bayesian network with n variables where CLG, logistic and multinomial distributions are allowed. We take the derivative of Q w. We skip some previous steps since they are the same. In a similar way as in Section 1. This does, unfortunately, make it difficult to calculate the expectations above due to their combination with the logistic function. It will, however, not be possible to find the roots of the equation, which points towards a generalized EM algorithm rather than standard EM algorithm.
Let see in more detail the calculation of equation 1. Calculation of the expectations in the MTE framework 1.
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