What is the math behind CTF and Deviance?
Quote 0 0
The CTF measures the quality of the representation of the Joint Probability Distribution by your network (with respect to the fully connected network).Contingency Table Fit:BayesiaLab's CTF is defined as: where: is the mean of the log-likelihood of the data given the fully unconnected network (UN) is the mean of the log-likelihood of the data given the evaluated network (BBN) is the mean of the log-likelihood of the data given the fully connected network (FCN)The fully connected network is a graph in which all nodes have a direct link with all other ones. Therefore, this is the exact representation of the chain rule, without any conditional independence assumptions in the representation of the joint probability distribution.[*:12270or5]C is equal to 100 when the joint probability distribution is represented without any approximation, i.e. the same log likelihood as the one obtained with the fully connected network[/*:m:12270or5][*:12270or5]C is equal to 0 when the joint probability distribution is represented by considering that all the variables are independent, i.e. the same joint probability distribution as the one obtained with the fully unconnected network[/*:m:12270or5]C can also be negative, if the parameters of the BBN do not correspond to the dataset.Deviance:Deviance is defined as: where N is the size of the dataset.Fully Unconnected Network:   Fully Connected Network:  BBN Learned:  Quote 0 0