Minimum bounding polytropes for estimation of max-linear Bayesian networks
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| Format: | Preprint |
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2025
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| _version_ | 1866912695886807040 |
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| author | Ferry, Kamillo |
| author_facet | Ferry, Kamillo |
| contents | Max-linear Bayesian networks are recursive max-linear structural equation models represented by an edge weighted directed acyclic graph (DAG). The identifiability and estimation of max-linear Bayesian networks is an intricate issue as Gissibl, Klüppelberg, and Lauritzen have shown. As such, a max-linear Bayesian network is generally unidentifiable and standard likelihood theory cannot be applied. We can associate tropical polyhedra to max-linear Bayesian networks. Using this, we investigate the minimum-ratio estimator proposed by Gissibl, Klüppelberg, and Lauritzen and give insight on the structure of minimal best-case samples for parameter recovery which we describe in terms of set covers of certain triangulations. We also combine previous work on estimating max-linear models from Tran, Buck, and Klüppelberg to apply our geometric approach to the structural inference of max-linear models. This is tested extensively on simulated data and on real world data set, the NHANES report for 2015--2016 and the upper Danube network data. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_05962 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Minimum bounding polytropes for estimation of max-linear Bayesian networks Ferry, Kamillo Methodology Combinatorics Statistics Theory 05C12, 14T90, 52B11, 62R01 Max-linear Bayesian networks are recursive max-linear structural equation models represented by an edge weighted directed acyclic graph (DAG). The identifiability and estimation of max-linear Bayesian networks is an intricate issue as Gissibl, Klüppelberg, and Lauritzen have shown. As such, a max-linear Bayesian network is generally unidentifiable and standard likelihood theory cannot be applied. We can associate tropical polyhedra to max-linear Bayesian networks. Using this, we investigate the minimum-ratio estimator proposed by Gissibl, Klüppelberg, and Lauritzen and give insight on the structure of minimal best-case samples for parameter recovery which we describe in terms of set covers of certain triangulations. We also combine previous work on estimating max-linear models from Tran, Buck, and Klüppelberg to apply our geometric approach to the structural inference of max-linear models. This is tested extensively on simulated data and on real world data set, the NHANES report for 2015--2016 and the upper Danube network data. |
| title | Minimum bounding polytropes for estimation of max-linear Bayesian networks |
| topic | Methodology Combinatorics Statistics Theory 05C12, 14T90, 52B11, 62R01 |
| url | https://arxiv.org/abs/2511.05962 |