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Pré-Publication, Document De Travail Année : 2023

Equivalence between conditional random fields and partially Markov models

Elie Azeraf
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Résumé

Hidden Markov models (HMM) have been used successfully in various applications for around sixty years. Moreover, conditional random fields (CRFs) are considered an alternative to HMMs and appear in the literature as different and somewhat competing models. It has recently been shown that basic linear chain CRFs (LC-CRFs), considered different from HMMs, are in fact equivalent to them in the sense that for each LC-CRF there exists an HMM, which can be specified, whose a posteriori distribution is identical to the given LC-CRF. In this article, we extend this result to general CRFs. We consider partially Markovian models (PMMs), which are sequentially defined models extending HMMs, and we show that they are equivalent to CRFs. Equivalence means that the posterior distributions of the PMMs are CRFs and, conversely, for each given CRF there exists a PMM - which we specify - whose posterior distribution is the given CRF. The first assertion is well known and the proof of the second constitutes the main contribution of this article. The advantage of presenting a CRF in its PMM form is that the latter is sequential, whereas its original former is not. This property is essential in certain sequential processing, such as filteri ng or forecasting.
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Dates et versions

hal-04280748 , version 1 (11-11-2023)
hal-04280748 , version 2 (15-11-2023)

Identifiants

  • HAL Id : hal-04280748 , version 2

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Elie Azeraf, Wojciech Pieczynski. Equivalence between conditional random fields and partially Markov models. 2023. ⟨hal-04280748v2⟩
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