{"ID":2844618,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.05962","arxiv_id":"2511.05962","title":"Minimum bounding polytropes for estimation of max-linear Bayesian networks","abstract":"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.","short_abstract":"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 networ...","url_abs":"https://arxiv.org/abs/2511.05962","url_pdf":"https://arxiv.org/pdf/2511.05962v1","authors":"[\"Kamillo Ferry\"]","published":"2025-11-08T10:34:32Z","proceeding":"stat.ME","tasks":"[\"stat.ME\",\"math.CO\",\"math.ST\"]","methods":"[]","has_code":false}