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Why does the ordering of variables affect the network's size?

  • A.The ordering determines which variables may be observed
  • B.A causal ordering usually needs fewer parents per node
  • C.The chain rule is exact only for one particular ordering
  • D.Later variables always require more parents than earlier ones

Answer: B

Listing causes before effects usually lets each node depend on few predecessors, whereas the reverse ordering forces dense connections that encode the same distribution far less compactly. Every ordering is exact, and observation is unrelated. That the same distribution may have a sparse or a dense representation, according to how it is written, is why structure learning and expert elicitation both begin by seeking the causal direction. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

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