Links

Contingency Table Fit

Definition

Contingency Table Fit (CTF) measures the quality of the representation of the Joint Probability Distribution by a Bayesian network
BB
compared to a complete (i.e., fully-connected) network
CC
.
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})}}
where
  • HU(D){{H_U}({\cal D})}
    is the entropy of the data with the unconnected network
    UU
    .
  • HB(D){{H_B}({\cal D})}
    is the entropy of the data with the evaluated network
    BB
    .
  • HC(D){{H_C}({\cal D})}
    is the entropy of the data with 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.

Interpretation

  • CB{C_B}
    is equal to 100 if the Joint Probability Distribution is represented without any approximation, i.e., the entropy of the evaluated network
    BB
    is the same as that obtained with the complete network
    CC
    .
  • CB{C_B}
    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
    UU
    .
  • CB{C_B}
    can also be negative if the parameters of network
    BB
    do not correspond to the dataset.