One of the main assumptions of the naive Bayes model is that the features are independent. This allows probabilities to be estimated. However, often times it is understood that this assumption doesn't hold in the data. Naive Bayes is, however, still used for applications like text classification because it still provides "good results."
My question is:
1) Is there any way to check how well the assumption holds? I.e., can I test for conditional independence?
2) Is there a way to determine what "good results" are. I.e., are "good results" from a naive Bayes model, vs any other model, based on things like accuracy/how well the model cross validates on training data?