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I have a Bayesian network with the following structure:

Bayesian network

Each node has two states, true (T) and false (F). Evidence can be observed for the nodes at the top and there's a node for the final result at the bottom.

I would like to find out which of the influence nodes at the top has the largest influence on the result node at the bottom. For example, I would like to know whether evidence for "Influence A" (true = 1.0, i.e., increasing its probability by 0.2) increases the probability of the result being true more than evidence for "Influence B" (increasing its probability by 0.9), and so on.

Given $n$ influence nodes, I currently apply an inference algorithm on the network $n$ times, each time with different evidence, and observe for which evidence the probability of the result being true is the highest. However, I'm wondering if there is a more efficient algorithm to get the same result because the network is very large and inference takes a long time to compute.

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