Linear chain conditional random fields, hidden Markov models, and related classifiers
This clarifies theoretical relationships between widely used models in fields like Natural Language Processing, but it is incremental as it builds on existing knowledge without introducing new methods.
The paper demonstrates that Linear-Chain Conditional Random Fields (LC-CRFs) are equivalent to Hidden Markov Models (HMMs) in terms of posterior distributions, and reformulates generative Bayesian classifiers from HMMs into discriminative forms, showing that switching from HMMs to CRFs is unnecessary in some cases.
Practitioners use Hidden Markov Models (HMMs) in different problems for about sixty years. Besides, Conditional Random Fields (CRFs) are an alternative to HMMs 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 to them 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 show that it is possible to reformulate the generative Bayesian classifiers Maximum Posterior Mode (MPM) and Maximum a Posteriori (MAP) used in HMMs, as discriminative ones. The last point is of importance in many fields, especially in Natural Language Processing (NLP), as it shows that in some situations dropping HMMs in favor of CRFs was not necessary.