CRFs directly estimate the posterior/conditional model you care about (it tells you how to tag things), whereas a HMM estimates the joint model which you then u

CRFs directly estimate the posterior/conditional model you care about (it tells you how to tag things), whereas a HMM estimates the joint model which you then use for inference. The general feeling is that it is actually easier to learn the posterior model than then joint model. (And the insight of linear models like support vector machines is that it is easier to just learn the most likely label than it is to estimate the label-given-observation probability distribution.) In fact a linear-chain CRF is little more than the discriminative version of an HMM. (And an HMM is just a sequential naïve Bayes classifier, and a linear-chain CRF is just a sequential logistic regression classifier. And, while I'm at it, a max-margin markov network is just a sequential support vector machine.)