Deviance

Context

  • The Deviance measure is based on the difference between the Entropy of the to-be-evaluated network BB and the Entropy of the complete (i.e., fully connected) network CC.

  • The closer the Deviance value is to 0, the better the network BB represents the dataset.

Definition

Deviance is formally defined as:

DB=2Nร—lnโก(2)ร—(HB(D)โˆ’HC(D)){D_B} = 2N \times \ln (2) \times \left( {{H_B}({\cal D}) - {H_C}({\cal D})} \right)

where

  • HB(D){{H_B}({\cal D})} is the Entropy of the dataset given the to-be-evaluated network BB.

  • HC(D){{H_C}({\cal D})} is the Entropy of the dataset given the complete (i.e., fully connected) network CC. In the complete network, all nodes are directly connected to all other nodes. Therefore, the complete network CC is an exact representation of the chain rule. As such, it does not utilize any conditional independence assumptions for representing the Joint Probability Distribution.

  • NN is the size of the dataset.

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