Contingency Table Fit

Definition
Contingency Table Fit (CTF) measures the quality of the representation of the Joint Probability Distribution by a Bayesian network BBB
 compared to a complete (i.e., fully-connected) network CCC
.
BayesiaLab's CTF is defined as:
CB=100×HU(D)−HB(D)HU(D)−HC(D){C_B} = 100 \times \frac{{{H_U}({\cal D}) - {H_B}({\cal D})}}{{{H_U}({\cal D}) - {H_C}({\cal D})}}CB​=100×HU​(D)−HC​(D)HU​(D)−HB​(D)​
where
​HU(D){{H_U}({\cal D})}HU​(D)
 is the entropy of the data with the unconnected network UUU
.
​HB(D){{H_B}({\cal D})}HB​(D)
 is the entropy of the data with the evaluated network BBB
.
​HC(D){{H_C}({\cal D})}HC​(D)
 is the entropy of the data with 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. 
Interpretation
​CB{C_B}CB​
 is equal to 100 if the Joint Probability Distribution is represented without any approximation, i.e., the entropy of the evaluated network BBB
 is the same as that obtained with the complete network CCC
.
​CB{C_B}CB​
 is equal to 0 if the Joint Probability Distribution is represented by considering that all the variables are independent, i.e., the entropy of the evaluated network B is the same as the one obtained with the unconnected network UUU
.
​CB{C_B}CB​
 can also be negative if the parameters of network BBB
 do not correspond to the dataset.
Information Gain
Deviance
Last modified 1mo ago