# Deviance

### Context

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

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

### Definition

Deviance is formally defined as:

${D_B} = 2N \times \ln (2) \times \left( {{H_B}({\cal D}) - {H_C}({\cal D})} \right)$

where

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

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

• $N$ is the size of the dataset.

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