Bayes net criteria

The formal criteria for a Probabilistic Graphical Model (PGM) to be a Bayesian network (mostly useful for proofs):

• The state space must be finite

• Each node is a variable

  • If the node doesn’t have a parent then it has a probability function (called a potential)

  Note this is a marginal distribution for the variable

• If the node has parents , then it has a potential

• The factorization represented by the BN is minimal
  • The nodes are ordered so that a node’s parents are a subset of the nodes before it in the ordering
  • for a node , its set of parents is the smallest set so that is conditionally independent of its non-parents.

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References

@koski2011