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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?

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1) There is no single answer to this question. A good metric for linear dependence is a correlation matrix. i.e. cor(x) in R. If the features are linearly independent, they are uncorrelated, hence the non-diagonal entries of the correlation matrix should be close to zero. See here for a discussion of why naive bayes does well even when its assumptions are violated.

2) Again, there is no single answer to this question. The most common way to compare machine learning models is to see how well they do on held out data and the most common metric is AUC.

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