Causal structure learning in directed, possibly cyclic, graphical models
We consider the problem of learning a directed graph G⋆{G}^{\star } from observational data. We assume that the distribution that gives rise to the samples is Markov and faithful to the graph G⋆{G}^{\star } and that there are no unobserved variables. We do not rely on any further assumptions regardi...
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| Language: | English |
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De Gruyter
2025-04-01
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| Series: | Journal of Causal Inference |
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| Online Access: | https://doi.org/10.1515/jci-2024-0037 |
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| author | Semnani Pardis Robeva Elina |
| author_facet | Semnani Pardis Robeva Elina |
| author_sort | Semnani Pardis |
| collection | DOAJ |
| description | We consider the problem of learning a directed graph G⋆{G}^{\star } from observational data. We assume that the distribution that gives rise to the samples is Markov and faithful to the graph G⋆{G}^{\star } and that there are no unobserved variables. We do not rely on any further assumptions regarding the graph or the distribution of the variables. Particularly, we allow for directed cycles in G⋆{G}^{\star } and work in the fully nonparametric setting. Given the set of conditional independence statements satisfied by the distribution, we aim to find a directed graph, which satisfies the same dd-separation statements as G⋆{G}^{\star }. We propose a hybrid approach consisting of two steps. We first find a partially ordered partition of the vertices of G⋆{G}^{\star } by optimizing a certain score in a greedy fashion. We prove that any optimal partition uniquely characterizes the Markov equivalence class of G⋆{G}^{\star }. Given an optimal partition, we propose an algorithm for constructing a graph in the Markov equivalence class of G⋆{G}^{\star } whose strongly connected components correspond to the elements of the partition, and which are partially ordered according to the partial order of the partition. Our algorithm comes in two versions – one that is provably correct and another one that performs fast in practice. |
| format | Article |
| id | doaj-art-59525e3512464a389bd4209f4cbdd044 |
| institution | OA Journals |
| issn | 2193-3685 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Journal of Causal Inference |
| spelling | doaj-art-59525e3512464a389bd4209f4cbdd0442025-08-20T01:54:19ZengDe GruyterJournal of Causal Inference2193-36852025-04-011316012010.1515/jci-2024-0037Causal structure learning in directed, possibly cyclic, graphical modelsSemnani Pardis0Robeva Elina1Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, CanadaDepartment of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, CanadaWe consider the problem of learning a directed graph G⋆{G}^{\star } from observational data. We assume that the distribution that gives rise to the samples is Markov and faithful to the graph G⋆{G}^{\star } and that there are no unobserved variables. We do not rely on any further assumptions regarding the graph or the distribution of the variables. Particularly, we allow for directed cycles in G⋆{G}^{\star } and work in the fully nonparametric setting. Given the set of conditional independence statements satisfied by the distribution, we aim to find a directed graph, which satisfies the same dd-separation statements as G⋆{G}^{\star }. We propose a hybrid approach consisting of two steps. We first find a partially ordered partition of the vertices of G⋆{G}^{\star } by optimizing a certain score in a greedy fashion. We prove that any optimal partition uniquely characterizes the Markov equivalence class of G⋆{G}^{\star }. Given an optimal partition, we propose an algorithm for constructing a graph in the Markov equivalence class of G⋆{G}^{\star } whose strongly connected components correspond to the elements of the partition, and which are partially ordered according to the partial order of the partition. Our algorithm comes in two versions – one that is provably correct and another one that performs fast in practice.https://doi.org/10.1515/jci-2024-0037causal discoverydirected cyclic graphsmarkov equivalencefaithfulnessd-separationsconditional independence62d2062h2205c20 |
| spellingShingle | Semnani Pardis Robeva Elina Causal structure learning in directed, possibly cyclic, graphical models Journal of Causal Inference causal discovery directed cyclic graphs markov equivalence faithfulness d-separations conditional independence 62d20 62h22 05c20 |
| title | Causal structure learning in directed, possibly cyclic, graphical models |
| title_full | Causal structure learning in directed, possibly cyclic, graphical models |
| title_fullStr | Causal structure learning in directed, possibly cyclic, graphical models |
| title_full_unstemmed | Causal structure learning in directed, possibly cyclic, graphical models |
| title_short | Causal structure learning in directed, possibly cyclic, graphical models |
| title_sort | causal structure learning in directed possibly cyclic graphical models |
| topic | causal discovery directed cyclic graphs markov equivalence faithfulness d-separations conditional independence 62d20 62h22 05c20 |
| url | https://doi.org/10.1515/jci-2024-0037 |
| work_keys_str_mv | AT semnanipardis causalstructurelearningindirectedpossiblycyclicgraphicalmodels AT robevaelina causalstructurelearningindirectedpossiblycyclicgraphicalmodels |