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Practitioners use Hidden Markov Models (HMMs) in different problems for aboutsixty years. Besides, Conditional Random Fields (CRFs) are an alternative toHMMs and appear in the literature as different and somewhat concurrent models.We propose two contributions. First, we show that basic Linear-Chain CRFs(LC-CRFs), considered as different from the HMMs, are in fact equivalent tothem in the sense that for each LC-CRF there exists a HMM - that we specify -whom posterior distribution is identical to the given LC-CRF. Second, we showthat it is possible to reformulate the generative Bayesian classifiers MaximumPosterior Mode (MPM) and Maximum a Posteriori (MAP) used in HMMs, asdiscriminative ones. The last point is of importance in many fields, especiallyin Natural Language Processing (NLP), as it shows that in some situationsdropping HMMs in favor of CRFs was not necessary.

Linear chain conditional random fields, hidden Markov models, and related classifiers