How do I derive the EM training equations for a noisy-OR Bayesian network?I am familiar with one solution to these equations.  If I remember correctly, the result is:Given a model with link weights $$p_{ij} = 1-e^{-w_{ij}}$$ between nodes $i$ and $j$.  Then, for each training example fix the input variables, and use the model to generate some configurations over latent variables.  For each configuration where $T$ is the set of variables that are true, the configuration probability probability is $q$:\begin{align}q_j &= 1-\prod_{i\in T} (1-p_{ij})=1-e^{-\sum_{i\in T}w_{ij}}\newlineq &= \prod_{j \in T}q_j\prod_{j \notin T}(1-q_j)\end{align}The E-step comprises updating counts:Add $q$ to $x_i$: if $i \in T$.Add $$q\frac{p_{ij}}{q_j}\qquad\qquad(1)$$to $l_{ij}$ if $i, j \in T$ and there is a link from $i$ to $j$.The M-step is to let each new link weight (from node $i$ to node $j$) be:$$\frac{l_{ij}}{x_i}$$When I tried to derive these equations, I wasn't able to generate equation (1).
Derivation of Expected-Maximization training equations for a noisy-OR Bayesian network
machine learning