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I am working through the course Probabilistic Graphical Models.

A CRF calculates the conditional probability distribution, i.e P(Y | X1, .., XN). The following picture shows an example how the CRF is calculated. 'I' in the picture is the indicator function

enter image description here

The question I would like to ask is:

"If you had a naive bayes model and you wanted to calculate the conditional distributions for a given set of features, we would have to calculate the joint distribution through factor multiplication and then marginalize over the features. How is this fundamentally different than the above example given for the logistic function as a simple CRF?"

One answer is the factors are not normalized in the case of CRF but I don't think this is correct.

Would be grateful for any help.

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Certainly a major difference is that the CRF model doesn't make the naive Bayes assumption. The distinguishing characteristic of Naive Bayes is that you assume that the features are independent given the class label, which simplifies the inference greatly. The CRF doesn't make this assumption anywhere.

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  • $\begingroup$ Yes, agreed, there is a difference in assumption but the way we calculate the probabilities, in both the cases are same (similar to be precise as factors can be unnormalized in CRFs). So though we assume differently but we end up doing the same calculation. $\endgroup$
    – Hrushi
    Commented Aug 29, 2020 at 15:53

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