The two filter formula reconsidered: Smoothing in partially observed Gauss--Markov models without information parametrization
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916635413053440 |
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| author | Tronarp, Filip |
| author_facet | Tronarp, Filip |
| contents | In this article, the two filter formula is re-examined in the setting of partially observed Gauss--Markov models. It is traditionally formulated as a filter running backward in time, where the Gaussian density is parametrized in ``information form''. However, the quantity in the backward recursion is strictly speaking not a distribution, but a likelihood. Taking this observation seriously, a recursion over log-quadratic likelihoods is formulated instead, which obviates the need for ``information'' parametrization. In particular, it greatly simplifies the square-root formulation of the algorithm. Furthermore, formulae are given for producing the forward Markov representation of the a posteriori distribution over paths from the proposed likelihood representation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_21116 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The two filter formula reconsidered: Smoothing in partially observed Gauss--Markov models without information parametrization Tronarp, Filip Methodology Machine Learning In this article, the two filter formula is re-examined in the setting of partially observed Gauss--Markov models. It is traditionally formulated as a filter running backward in time, where the Gaussian density is parametrized in ``information form''. However, the quantity in the backward recursion is strictly speaking not a distribution, but a likelihood. Taking this observation seriously, a recursion over log-quadratic likelihoods is formulated instead, which obviates the need for ``information'' parametrization. In particular, it greatly simplifies the square-root formulation of the algorithm. Furthermore, formulae are given for producing the forward Markov representation of the a posteriori distribution over paths from the proposed likelihood representation. |
| title | The two filter formula reconsidered: Smoothing in partially observed Gauss--Markov models without information parametrization |
| topic | Methodology Machine Learning |
| url | https://arxiv.org/abs/2502.21116 |