{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/efficient-bayesian-network-structure-learning","title":"Efficient Bayesian network structure learning via local Markov boundary search","arxiv_id":"2110.06082","date":"2021-10-12","proceeding":"NeurIPS 2021 12","authors":["Ming Gao","Bryon Aragam"],"abstract":"We analyze the complexity of learning directed acyclic graphical models from observational data in general settings without specific distributional assumptions. Our approach is information-theoretic and uses a local Markov boundary search procedure in order to recursively construct ancestral sets in the underlying graphical model. Perhaps surprisingly, we show that for certain graph ensembles, a simple forward greedy search algorithm (i.e. without a backward pruning phase) suffices to learn the Markov boundary of each node. This substantially improves the sample complexity, which we show is at most polynomial in the number of nodes. This is then applied to learn the entire graph under a novel identifiability condition that generalizes existing conditions from the literature. As a matter of independent interest, we establish finite-sample guarantees for the problem of recovering Markov boundaries from data. Moreover, we apply our results to the special case of polytrees, for which the assumptions simplify, and provide explicit conditions under which polytrees are identifiable and learnable in polynomial time. We further illustrate the performance of the algorithm, which is easy to implement, in a simulation study. Our approach is general, works for discrete or continuous distributions without distributional assumptions, and as such sheds light on the minimal assumptions required to efficiently learn the structure of directed graphical models from data.","url_abs":"https://arxiv.org/abs/2110.06082v2","url_pdf":"https://arxiv.org/pdf/2110.06082v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"efficient-bayesian-network-structure-learning","repo_url":"https://github.com/minggao97/tam","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"Apache-2.0"}}],"tasks":[],"methods":[{"method_slug":"pruning","method_name":"Pruning"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2110.06082","atlas_url":"https://app.syntology.ai/?focus=2110.06082","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2110.06082"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"deterministic:regex_extraction","url":"https://github.com/MingGao97/TAM","reach":{"status":"ok","spdx":"Apache-2.0"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/minggao97/tam","reach":{"status":"ok","spdx":"Apache-2.0"}}],"summary":{"ran_fixture":2,"ran_honours":1,"unverified":2},"by_repo_kind":{"official":{"samples":5,"ran":3,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"39e54a6aa658001e","entry":"compute_caus_order","repo":"MingGao97/TAM","repo_kind":"official","path":"utils.py","file_url":"https://github.com/MingGao97/TAM/blob/HEAD/utils.py","link_basis":"first_harvest_node","language":"python","status":"ran_fixture","verification_level":1,"contract_check":"RAISES","metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"Apache-2.0","inline_ok":true,"mcp_get_code":{"code_sha256":"39e54a6aa658001e"}},{"code_sha256_prefix":"9f398ccc9700fa6f","entry":"find_pa","repo":"MingGao97/TAM","repo_kind":"official","path":"utils.py","file_url":"https://github.com/MingGao97/TAM/blob/HEAD/utils.py","link_basis":"first_harvest_node","language":"python","status":"ran_honours","verification_level":1,"contract_check":"HONOURS","metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"Apache-2.0","inline_ok":true,"mcp_get_code":{"code_sha256":"9f398ccc9700fa6f"}},{"code_sha256_prefix":"63093a724f8c2078","entry":"test_order","repo":"MingGao97/TAM","repo_kind":"official","path":"utils.py","file_url":"https://github.com/MingGao97/TAM/blob/HEAD/utils.py","link_basis":"first_harvest_node","language":"python","status":"ran_fixture","verification_level":1,"contract_check":"RAISES","metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"Apache-2.0","inline_ok":true,"mcp_get_code":{"code_sha256":"63093a724f8c2078"}},{"code_sha256_prefix":"b7e3082511698ab2","entry":"est_entropy","repo":"MingGao97/TAM","repo_kind":"official","path":"tam.py","file_url":"https://github.com/MingGao97/TAM/blob/HEAD/tam.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"Apache-2.0","inline_ok":true,"mcp_get_code":{"code_sha256":"b7e3082511698ab2"}},{"code_sha256_prefix":"7314ae37712b997a","entry":"findPPS","repo":"MingGao97/TAM","repo_kind":"official","path":"tam.py","file_url":"https://github.com/MingGao97/TAM/blob/HEAD/tam.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"Apache-2.0","inline_ok":true,"mcp_get_code":{"code_sha256":"7314ae37712b997a"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}