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

arXiv: https://arxiv.org/abs/2301.01293 · HTML: https://mlsanity.com/paper/2301.01293/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 24 references that are in the map.
- First posted on arXiv 3 Jan 2023.

## Builds on (most cited first, 2 of 2)

- [Hidden Markov Chains, Entropic Forward-Backward, and Part-Of-Speech Tagging](https://mlsanity.com/paper/2005.10629/) (2020)
- [On equivalence between linear-chain conditional random fields and hidden Markov chains](https://mlsanity.com/paper/2111.07376/) (2021)

## Abstract (arXiv)

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.