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.

翻译：实践者使用隐马尔可夫模型（HMMs）解决各类问题已有约六十年之久。此外，条件随机场（CRFs）作为HMMs的替代方案出现在文献中，被视为不同且略具竞争性的模型。我们提出两项贡献：首先，揭示通常认为与HMMs不同的基础线性链条件随机场（LC-CRFs），实则与之等价——即对于每个LC-CRF，存在一个我们明确指定的HMM，其后验分布与给定LC-CRF完全相同。其次，论证可将HMMs中使用的生成式贝叶斯分类器——最大后验模式（MPM）和最大后验概率（MAP）——重构为判别式形式。最后一点在诸多领域（尤其是自然语言处理NLP）具有重要意义，因为它表明在某些情境下，将HMMs替换为CRFs并非必要。