{"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/verification-and-search-algorithms-for-causal","title":"Verification and search algorithms for causal DAGs","arxiv_id":"2206.15374","date":"2022-06-30","proceeding":null,"authors":["Davin Choo","Kirankumar Shiragur","Arnab Bhattacharyya"],"abstract":"We study two problems related to recovering causal graphs from interventional data: (i) $\\textit{verification}$, where the task is to check if a purported causal graph is correct, and (ii) $\\textit{search}$, where the task is to recover the correct causal graph. For both, we wish to minimize the number of interventions performed. For the first problem, we give a characterization of a minimal sized set of atomic interventions that is necessary and sufficient to check the correctness of a claimed causal graph. Our characterization uses the notion of $\\textit{covered edges}$, which enables us to obtain simple proofs and also easily reason about earlier known results. We also generalize our results to the settings of bounded size interventions and node-dependent interventional costs. For all the above settings, we provide the first known provable algorithms for efficiently computing (near)-optimal verifying sets on general graphs. For the second problem, we give a simple adaptive algorithm based on graph separators that produces an atomic intervention set which fully orients any essential graph while using $\\mathcal{O}(\\log n)$ times the optimal number of interventions needed to $\\textit{verify}$ (verifying size) the underlying DAG on $n$ vertices. This approximation is tight as $\\textit{any}$ search algorithm on an essential line graph has worst case approximation ratio of $\\Omega(\\log n)$ with respect to the verifying size. With bounded size interventions, each of size $\\leq k$, our algorithm gives an $\\mathcal{O}(\\log n \\cdot \\log k)$ factor approximation. Our result is the first known algorithm that gives a non-trivial approximation guarantee to the verifying size on general unweighted graphs and with bounded size interventions.","url_abs":"https://arxiv.org/abs/2206.15374v2","url_pdf":"https://arxiv.org/pdf/2206.15374v2.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":"verification-and-search-algorithms-for-causal","repo_url":"https://github.com/cxjdavin/verification-and-search-algorithms-for-causal-dags","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"verification-and-search-algorithms-for-causal","repo_url":"https://github.com/cxjdavin/active-causal-structure-learning-with-advice","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"verification-and-search-algorithms-for-causal","repo_url":"https://github.com/cxjdavin/adaptivity-complexity-for-causal-graph-discovery","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"verification-and-search-algorithms-for-causal","repo_url":"https://github.com/cxjdavin/subset-verification-and-search-algorithms-for-causal-dags","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2206.15374","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2206.15374"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+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. 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