Deviance

Context
The Deviance measure is based on the difference between the Entropy of the to-be-evaluated network BBB
 and the Entropy of the complete (i.e., fully connected) network CCC
. 
The closer the Deviance value is to 0, the better the network BBB
 represents the dataset.
Definition
Deviance is formally defined as:
​DB=2N×ln⁡(2)×(HB(D)−HC(D)){D_B} = 2N \times \ln (2) \times \left( {{H_B}({\cal D}) - {H_C}({\cal D})} \right)DB​=2N×ln(2)×(HB​(D)−HC​(D))
​
where 
​HB(D){{H_B}({\cal D})}HB​(D)
 is the Entropy of the dataset given the to-be-evaluated network BBB
.
​HC(D){{H_C}({\cal D})}HC​(D)
 is the Entropy of the dataset given the complete (i.e., fully connected) network CCC
. In the complete network, all nodes are directly connected to all other nodes. Therefore, the complete network CCC
 is an exact representation of the chain rule. As such, it does not utilize any conditional independence assumptions for representing the Joint Probability Distribution.
​NNN
 is the size of the dataset.

Contingency Table Fit

Markov Blanket

Last modified 1mo ago