# On equivalence between linear-chain conditional random fields and hidden Markov chains

arXiv: https://arxiv.org/abs/2111.07376 · HTML: https://mlsanity.com/paper/2111.07376/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 28 references that are in the map.
- First posted on arXiv 14 Nov 2021.

## Builds on (most cited first, 3 of 3)

- [Hidden Markov Chains, Entropic Forward-Backward, and Part-Of-Speech Tagging](https://mlsanity.com/paper/2005.10629/) (2020)
- [Introducing the Hidden Neural Markov Chain framework](https://mlsanity.com/paper/2102.11038/) (2021)
- [Highly Fast Text Segmentation With Pairwise Markov Chains](https://mlsanity.com/paper/2102.11037/) (2021)

## Built on by (most cited first, 1 of 1)

- [Linear chain conditional random fields, hidden Markov models, and related classifiers](https://mlsanity.com/paper/2301.01293/) (2023)

## Abstract (arXiv)

Practitioners successfully use hidden Markov chains (HMCs) in different problems for about sixty years. HMCs belong to the family of generative models and they are often compared to discriminative models, like conditional random fields (CRFs). Authors usually consider CRFs as quite different from HMCs, and CRFs are often presented as interesting alternative to HMCs. In some areas, like natural language processing (NLP), discriminative models have completely supplanted generative models. However, some recent results show that both families of models are not so different, and both of them can lead to identical processing power. In this paper we compare the simple linear-chain CRFs to the basic HMCs. We show that HMCs are identical to CRFs in that for each CRF we explicitly construct an HMC having the same posterior distribution. Therefore, HMCs and linear-chain CRFs are not different but just differently parametrized models.