# Contingency Table Fit

**Contingency Table Fit (CTF)**measures the quality of the representation of the Joint Probability Distribution by a Bayesian network

$B$

compared to a complete (i.e., fully-connected) network $C$

.BayesiaLab's

**CTF**is defined as:${C_B} = 100 \times \frac{{{H_U}({\cal D}) - {H_B}({\cal D})}}{{{H_U}({\cal D}) - {H_C}({\cal D})}}$

where

- ${{H_U}({\cal D})}$is the entropy of the data with the unconnected network$U$.
- ${{H_B}({\cal D})}$is the entropy of the data with the evaluated network$B$.
- ${{H_C}({\cal D})}$is the entropy of the data with 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.

- ${C_B}$is equal to 100 if the Joint Probability Distribution is represented without any approximation, i.e., the entropy of the evaluated network$B$is the same as that obtained with the complete network$C$.
- ${C_B}$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$U$.
- ${C_B}$can also be negative if the parameters of network$B$do not correspond to the dataset.

Last modified 7mo ago