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I am learning about probabilistic graphical models and I was wondering if there is an example explaining the math behind conditional random fields. Looking solely on the formula, I have no idea what we actually do. I found a lot of examples for the hidden Markov model. There is a part speech-tag task where we have to find the tags for the sentence "flies like a flower". On these slides (slide 8) Ambiguity Resolution: Statistical Method-Prof. Ahmed Rafea, an HMM is used to find the correct tags. How would I transform this model into a CRF and how would I apply the math?

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CRF is for HMM in sequences classification as Logistic Regression is for Naive Bayes for simple classification. For a in depth difference between them I strongly suggest you to read the classical Sutton article "An Introduction to Conditional Random Fields". For a more practical example explaining how to apply the math I suggest you to read this article.

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