What happens if we flip the arrows in a Naive Bayes classifier? To clarify - from what I have found naive Bayes is defined for the following network structure:
I'm interested to understand what happens if instead from y->x the child will be y. As shown in the following:
I'm not entirely sure if we get the same results as a regular naive Bayes classifier (intuitively we don't), and if not how to estimate both the likelihood of the network and the parameters?
For further clarification: lets say there is a training set of size n; each data point consisting of (x,y) where x is a vector of size m of binary values and y is the class and is also binary. E.g. (0,1,0,1,1) where the last index is the class. I'm trying to figure out the likelihood of the network (where y is the child) and how to estimate the parameters in the case of y being the child.