Comparing CRF and HMM
The cost/benefit analysis of discriminative models relative to generative models applies to the comparison of the conditional random field with the hidden Markov model.
Contrary to the hidden Markov model, the conditional random field does not require the observations to be independent (conditional probability). The conditional random field can be regarded as a generalization of the HMM by extending the transition probabilities to arbitrary feature functions that can depend on the input sequence. The HMM assumes the transition probabilities matrix to be constant.
The HMM learns the transition probabilities aij on its own by processing more training data. The HMM can be regarded as a special case of CRF where the probabilities used in the state transition are constant.
