{"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/adaptivity-complexity-for-causal-graph","title":"Adaptivity Complexity for Causal Graph Discovery","arxiv_id":"2306.05781","date":"2023-06-09","proceeding":null,"authors":["Davin Choo","Kirankumar Shiragur"],"abstract":"Causal discovery from interventional data is an important problem, where the task is to design an interventional strategy that learns the hidden ground truth causal graph $G(V,E)$ on $|V| = n$ nodes while minimizing the number of performed interventions. Most prior interventional strategies broadly fall into two categories: non-adaptive and adaptive. Non-adaptive strategies decide on a single fixed set of interventions to be performed while adaptive strategies can decide on which nodes to intervene on sequentially based on past interventions. While adaptive algorithms may use exponentially fewer interventions than their non-adaptive counterparts, there are practical concerns that constrain the amount of adaptivity allowed. Motivated by this trade-off, we study the problem of $r$-adaptivity, where the algorithm designer recovers the causal graph under a total of $r$ sequential rounds whilst trying to minimize the total number of interventions. For this problem, we provide a $r$-adaptive algorithm that achieves $O(\\min\\{r,\\log n\\} \\cdot n^{1/\\min\\{r,\\log n\\}})$ approximation with respect to the verification number, a well-known lower bound for adaptive algorithms. Furthermore, for every $r$, we show that our approximation is tight. Our definition of $r$-adaptivity interpolates nicely between the non-adaptive ($r=1$) and fully adaptive ($r=n$) settings where our approximation simplifies to $O(n)$ and $O(\\log n)$ respectively, matching the best-known approximation guarantees for both extremes. Our results also extend naturally to the bounded size interventions.","url_abs":"https://arxiv.org/abs/2306.05781v1","url_pdf":"https://arxiv.org/pdf/2306.05781v1.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":"adaptivity-complexity-for-causal-graph","repo_url":"https://github.com/cxjdavin/adaptivity-complexity-for-causal-graph-discovery","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"causal-discovery","task_name":"Causal Discovery"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2306.05781","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2306.05781"}},"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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