- #1
IttyBittyBit
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Let's say we have a bayesian network G. Consider a subset A of this network consisting of a set of nodes and all the edges between them. Assume, for the sake of simplicity, that all nodes in A are binary (either true or false) and strongly anticorrelated i.e. if anyone of the nodes in A are true, the probability of any other nodes in A being true is close to zero.
It seems it should be possible to 'approximate' A by replacing it with a single non-binary node with multiple states, each state representing one of the former binary nodes being true (and one state correspending to the occurrence where none of them were true). I want to know if this is a common technique and, if so, what kind of approximation error bounds can be expected. Of course in the general case this might be a bit complicated but I would also be interested in any specialized cases (such as the case where the probability function of each node can be separated into the product of functions of each of the nodes).
It seems it should be possible to 'approximate' A by replacing it with a single non-binary node with multiple states, each state representing one of the former binary nodes being true (and one state correspending to the occurrence where none of them were true). I want to know if this is a common technique and, if so, what kind of approximation error bounds can be expected. Of course in the general case this might be a bit complicated but I would also be interested in any specialized cases (such as the case where the probability function of each node can be separated into the product of functions of each of the nodes).