# On Equivalence between Linear-chain Conditional Random Fields and Hidden Markov Chains

### Elie Azeraf, Elie Azeraf, Emmanuel Monfrini, Wojciech Pieczynski

#### 2022

#### Abstract

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 alternatives 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.

Download#### Paper Citation

#### in Harvard Style

Azeraf E., Monfrini E. and Pieczynski W. (2022). **On Equivalence between Linear-chain Conditional Random Fields and Hidden Markov Chains**. In *Proceedings of the 14th International Conference on Agents and Artificial Intelligence - Volume 3: ICAART,* ISBN 978-989-758-547-0, pages 725-728. DOI: 10.5220/0010897400003116

#### in Bibtex Style

@conference{icaart22,

author={Elie Azeraf and Emmanuel Monfrini and Wojciech Pieczynski},

title={On Equivalence between Linear-chain Conditional Random Fields and Hidden Markov Chains},

booktitle={Proceedings of the 14th International Conference on Agents and Artificial Intelligence - Volume 3: ICAART,},

year={2022},

pages={725-728},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0010897400003116},

isbn={978-989-758-547-0},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 14th International Conference on Agents and Artificial Intelligence - Volume 3: ICAART,

TI - On Equivalence between Linear-chain Conditional Random Fields and Hidden Markov Chains

SN - 978-989-758-547-0

AU - Azeraf E.

AU - Monfrini E.

AU - Pieczynski W.

PY - 2022

SP - 725

EP - 728

DO - 10.5220/0010897400003116