{"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/learning-causal-graphs-with-small","title":"Learning Causal Graphs with Small Interventions","arxiv_id":"1511.00041","date":"2015-10-30","proceeding":"NeurIPS 2015 12","authors":["Karthikeyan Shanmugam","Murat Kocaoglu","Alexandros G. Dimakis","Sriram Vishwanath"],"abstract":"We consider the problem of learning causal networks with interventions, when\neach intervention is limited in size under Pearl's Structural Equation Model\nwith independent errors (SEM-IE). The objective is to minimize the number of\nexperiments to discover the causal directions of all the edges in a causal\ngraph. Previous work has focused on the use of separating systems for complete\ngraphs for this task. We prove that any deterministic adaptive algorithm needs\nto be a separating system in order to learn complete graphs in the worst case.\nIn addition, we present a novel separating system construction, whose size is\nclose to optimal and is arguably simpler than previous work in combinatorics.\nWe also develop a novel information theoretic lower bound on the number of\ninterventions that applies in full generality, including for randomized\nadaptive learning algorithms.\n  For general chordal graphs, we derive worst case lower bounds on the number\nof interventions. Building on observations about induced trees, we give a new\ndeterministic adaptive algorithm to learn directions on any chordal skeleton\ncompletely. In the worst case, our achievable scheme is an\n$\\alpha$-approximation algorithm where $\\alpha$ is the independence number of\nthe graph. We also show that there exist graph classes for which the sufficient\nnumber of experiments is close to the lower bound. In the other extreme, there\nare graph classes for which the required number of experiments is\nmultiplicatively $\\alpha$ away from our lower bound.\n  In simulations, our algorithm almost always performs very close to the lower\nbound, while the approach based on separating systems for complete graphs is\nsignificantly worse for random chordal graphs.","url_abs":"http://arxiv.org/abs/1511.00041v1","url_pdf":"http://arxiv.org/pdf/1511.00041v1.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":"learning-causal-graphs-with-small","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},{"paper_slug":"learning-causal-graphs-with-small","repo_url":"https://github.com/cxjdavin/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=1511.00041","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}