• Two common approaches to sequence modeling are a generative approach, HMM tagging, and a discriminative approach, CRF tagging. We will see a neural approach in following chapters. • The probabilities in HMM taggers are estimated by maximum likelihood estimation on tag-labeled training corpora. The Viterbi algorithm is used for decoding, finding the most likely tag sequence • Conditional Random Fields or CRF taggers train a log-linear model that can choose the best tag sequence given an observation sequence, based on features that condition on the output tag, the prior output tag, the entire input sequence, and the current timestep. They use the Viterbi algorithm for inference, to choose the best sequence of tags, and a version of the Forward-Backward algorithm (see Appendix A) for training.