{"type":"ScholarlyArticle","title":"Empirical Bayesian Approaches for Robust Constraint-based Causal Discovery under Insufficient Data","authors":[{"name":"Zijun Cui","slug":"zijun-cui","given":"Zijun","family":"Cui","affiliation":"Rensselaer Polytechnic Institute"},{"name":"Naiyu Yin","slug":"naiyu-yin","given":"Naiyu","family":"Yin","affiliation":"Rensselaer Polytechnic Institute"},{"name":"Yuru Wang","slug":"yuru-wang","given":"Yuru","family":"Wang","affiliation":"Northeast Normal University"},{"name":"Qiang Ji","slug":"qiang-ji","given":"Qiang","family":"Ji","affiliation":"Rensselaer Polytechnic Institute"}],"abstract":"Causal discovery is to learn cause-effect relationships among variables given observational data and is important for many applications. Existing causal discovery methods assume data sufficiency, which may not be the case in many real world datasets. As a result, many existing causal discovery methods can fail under limited data. In this work, we propose Bayesian-augmented frequentist independence tests to improve the performance of constraint-based causal discovery methods under insufficient data: 1) We firstly introduce a Bayesian method to estimate mutual information (MI), based on which we propose a robust MI based independence test; 2) Secondly, we consider the Bayesian estimation of hypothesis likelihood and incorporate it into a well-defined statistical test, resulting in a robust statistical testing based independence test. We apply proposed independence tests to constraint-based causal discovery methods and evaluate the performance on benchmark datasets with insufficient samples. Experiments show significant performance improvement in terms of both accuracy and efficiency over SOTA methods.","doi":"10.24963/ijcai.2022/672","url":"https://ijcai.org/proceedings/2022/672","pdf":"https://ijcai.org/proceedings/2022/0672.pdf","markdown":"https://ijcai.org/proceedings/2022/672.md","bibtex":"https://ijcai.org/proceedings/2022/bibtex/672","volume":{"slug":"2022","title":"Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2022","url":"https://ijcai.org/proceedings/2022/","year":2022,"location":"Vienna","dates":"23-29 July 2022","editors":"Luc De Raedt","isbn":"978-1-956792-00-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2022"},"section":"Uncertainty in AI","track":"Main Track","number":672,"pages":{"first":4850,"last":4856},"keywords":["Uncertainty in AI: Causality, Structural Causal Models and Causal Inference","Uncertainty in AI: Graphical Models"],"videos":[{"label":"Video #1","url":"https://slideslive.com/38986651","length_sec":80,"provider":"slideslive"},{"label":"Video #2","url":"https://slideslive.com/38984794","length_sec":354,"provider":"slideslive"}],"references":[{"position":1,"raw":"[Archer et al., 2013] Evan Archer, Il Park, and Jonathan Pil- low. Bayesian and quasi-bayesian estimators for mutual information from discrete data. Entropy, 15(5):1738- 1755, 2013.","title":"Evan Archer, Il Park, and Jonathan Pillow. Bayesian and quasi-bayesian estimators for mutual information from discrete data","authors":"Archer","year":"2013","venue":"Entropy","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Claassen and Heskes, 2012] Tom Claassen and Tom Hes- kes. A bayesian approach to constraint based causal in- ference. arXiv preprint arXiv:1210.4866, 2012.","title":"A bayesian approach to constraint based causal inference","authors":"Heskes Claassen, Tom Claassen, Tom Heskes","year":"2012","venue":null,"doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Colombo and Maathuis, 2014] Diego Colombo and Mar- loes H Maathuis. Order-independent constraint-based causal structure learning. The Journal of Machine Learn- ing Research, 15(1):3741-3782, 2014.","title":"Diego Colombo and Marloes H Maathuis. Order-independent constraint-based causal structure learning","authors":"Maathuis Colombo","year":"2014","venue":"The Journal of Machine Learning Research","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Colombo et al., 2012] Diego Colombo, Marloes H Maathuis, Markus Kalisch, and Thomas S Richard- son. Learning high-dimensional directed acyclic graphs with latent and selection variables. The Annals of Statistics, pages 294-321, 2012.","title":"Learning high-dimensional directed acyclic graphs with latent and selection variables","authors":"Colombo","year":"2012","venue":"The Annals of Statistics","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Gao and Ji, 2015] Tian Gao and Qiang Ji. Local causal dis- covery of direct causes and effects. Advances in Neural Information Processing Systems, 28:2512-2520, 2015.","title":"Local causal discovery of direct causes and effects","authors":"Tian Gao, Qiang Ji","year":"2015","venue":"Advances in Neural Information Processing Systems","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Geweke and Singleton, 1980] John F Geweke and Ken- neth J Singleton. Interpreting the likelihood ratio statistic in factor models when sample size is small. Journal of the American Statistical Association, 75(369):133-137, 1980.","title":"Interpreting the likelihood ratio statistic in factor models when sample size is small","authors":"F John, Kenneth J Geweke, Singleton","year":"1980","venue":"Journal of the American Statistical Association","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Glymour et al., 2019] Clark Glymour, Kun Zhang, and Pe- ter Spirtes. Review of causal discovery methods based on graphical models. Frontiers in genetics, 10:524, 2019.","title":"Review of causal discovery methods based on graphical models","authors":"Clark Glymour, Kun Zhang, Peter Spirtes","year":"2019","venue":"Frontiers in genetics","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Hutter, 2002] Marcus Hutter. Distribution of mutual infor- mation. In Advances in neural information processing sys- tems, pages 399-406, 2002.","title":"Distribution of mutual information","authors":"Marcus Hutter","year":"2002","venue":"Advances in neural information processing systems","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Kass and Raftery, 1995] Robert E Kass and Adrian E Raftery. Bayes factors. Journal of the american statistical association, 90(430):773-795, 1995.","title":"Bayes factors","authors":"E Robert, Adrian E Kass, Raftery","year":"1995","venue":"Journal of the american statistical association","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Li et al., 2019] Honghao Li, Vincent Cabeli, Nadir Sella, and Hervé Isambert. Constraint-based causal structure learning with consistent separating sets. In 33rd Confer- ence on Neural Information Processing Systems (NeurIPS 2019), 2019.","title":"Constraint-based causal structure learning with consistent separating sets","authors":"Li","year":"2019","venue":"33rd Conference on Neural Information Processing Systems","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Marx and Vreeken, 2018] Alexander Marx and Jilles Vreeken. Stochastic complexity for testing conditional in- dependence on discrete data. In NeurIPS 2018 Workshop on Causal Learning, 2018.","title":"Stochastic complexity for testing conditional independence on discrete data","authors":"Vreeken Marx, Alexander Marx, Jilles Vreeken","year":"2018","venue":"NeurIPS 2018 Workshop on Causal Learning","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[McDonald, 2009] John H McDonald. Handbook of biolog- ical statistics, volume 2. sparky house publishing Balti- more, MD, 2009.","title":"sparky house publishing Baltimore","authors":"H John, Mcdonald","year":"2009","venue":"Handbook of biological statistics","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Minka, 2000] Thomas Minka. Estimating a dirichlet distri- bution. Technical report, MIT, 2000.","title":"Estimating a dirichlet distribution","authors":"Thomas Minka","year":"2000","venue":null,"doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Mukherjee and Speed, 2007] Sach Mukherjee and Ter- ence P Speed. Markov chain monte carlo for structural inference with prior information. University of California; Berkeley, 2007.","title":"Sach Mukherjee and Terence P Speed. Markov chain monte carlo for structural inference with prior information","authors":"Speed Mukherjee","year":"2007","venue":null,"doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Natori et al., 2017] Kazuki Natori, Masaki Uto, and Maomi Ueno. Consistent learning bayesian networks with thou- sands of variables. In Advanced Methodologies for Bayesian Networks, pages 57-68, 2017.","title":"Consistent learning bayesian networks with thousands of variables","authors":"Kazuki Natori, Masaki Uto, Maomi Ueno","year":"2017","venue":"Advanced Methodologies for Bayesian Networks","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Ramsey et al., 2012] Joseph Ramsey, Jiji Zhang, and Pe- ter L Spirtes. Adjacency-faithfulness and conservative causal inference. arXiv preprint arXiv:1206.6843, 2012.","title":"Adjacency-faithfulness and conservative causal inference","authors":"Joseph Ramsey, Jiji Zhang, Peter L Spirtes","year":"2012","venue":null,"doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Rohekar et al., 2018] Raanan Y Rohekar, Yaniv Gurwicz, Shami Nisimov, Guy Koren, and Gal Novik. Bayesian structure learning by recursive bootstrap. In Advances in Neural Information Processing Systems, pages 10525- 10535, 2018.","title":"Bayesian structure learning by recursive bootstrap","authors":"Yaniv Raanan Y Rohekar, Shami Gurwicz, Guy Nisimov, Gal Koren, Novik","year":"2018","venue":"Advances in Neural Information Processing Systems","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Rohekar et al., 2020] Raanan Y Rohekar, Yaniv Gurwicz, Shami Nisimov, and Gal Novik. A single iterative step for anytime causal discovery. arXiv preprint arXiv:2012.07513, 2020.","title":"A single iterative step for anytime causal discovery","authors":"Yaniv Raanan Y Rohekar, Shami Gurwicz, Gal Nisimov, Novik","year":"2020","venue":null,"doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Sen et al., 2017] Rajat Sen, Ananda Theertha Suresh, Karthikeyan Shanmugam, Alexandros G Dimakis, and Sanjay Shakkottai. Model-powered conditional indepen- dence test. arXiv preprint arXiv:1709.06138, 2017.","title":"Model-powered conditional independence test","authors":"Rajat Sen, Ananda Theertha Suresh, Karthikeyan Shanmugam, Alexandros G Dimakis, Sanjay Shakkottai","year":"2017","venue":null,"doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Seok and Seon Kang, 2015] Junhee Seok and Yeong Seon Kang. Mutual information between discrete vari- ables with many categories using recursive adaptive partitioning. Scientific Reports, 5, 06 2015.","title":"Mutual information between discrete variables with many categories using recursive adaptive partitioning","authors":"Seon Seok, ; Kang, Junhee Seok, Yeong Seon Kang","year":"2015","venue":"Scientific Reports","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Spirtes et al., 2000] Peter Spirtes, Clark N Glymour, Richard Scheines, David Heckerman, Christopher Meek, Gregory Cooper, and Thomas Richardson. Causation, prediction, and search. MIT press, 2000.","title":"Causation, prediction, and search","authors":"Peter Spirtes, Richard Clark N Glymour, David Scheines, Christopher Heckerman, Gregory Meek, Thomas Cooper, Richardson","year":"2000","venue":null,"doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Spirtes, 2010] Peter Spirtes. Introduction to causal infer- ence. Journal of Machine Learning Research, 11(5), 2010.","title":"Peter Spirtes. Introduction to causal inference","authors":"Spirtes","year":"2010","venue":"Journal of Machine Learning Research","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Strobl et al., 2019] Eric V Strobl, Kun Zhang, and Shyam Visweswaran. Approximate kernel-based conditional in- dependence tests for fast non-parametric causal discovery. Journal of Causal Inference, 7(1), 2019.","title":"Approximate kernel-based conditional independence tests for fast non-parametric causal discovery","authors":"Eric V Strobl, Kun Zhang, Shyam Visweswaran","year":"2019","venue":"Journal of Causal Inference","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Tsamardinos et al., 2006a] Ioannis Tsamardinos, Laura E. Brown, and Constantin F. Aliferis. The max-min hill- climbing bayesian network structure learning algorithm. Machine Learning, 65(1):31-78, Oct 2006.","title":"The max-min hillclimbing bayesian network structure learning algorithm","authors":"Tsamardinos","year":"2006","venue":"Machine Learning","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Tsamardinos et al., 2006b] Ioannis Tsamardinos, Laura E Brown, and Constantin F Aliferis. The max-min hill- climbing bayesian network structure learning algorithm. Machine learning, 65(1):31-78, 2006.","title":"The max-min hillclimbing bayesian network structure learning algorithm","authors":"Tsamardinos","year":"2006","venue":"Machine learning","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Yang et al., 2021] Shuai Yang, Hao Wang, Kui Yu, Fuyuan Cao, and Xindong Wu. Towards efficient local causal structure learning, 2021.","title":"Towards efficient local causal structure learning","authors":"Shuai Yang, Hao Wang, Kui Yu, Fuyuan Cao, Xindong Wu","year":"2021","venue":null,"doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Yehezkel and Lerner, 2009] Raanan Yehezkel and Boaz Lerner. Bayesian network structure learning by recursive autonomy identification. Journal of Machine Learning Re- search, 10(Jul):1527-1570, 2009.","title":"Bayesian network structure learning by recursive autonomy identification","authors":"Lerner Yehezkel, Raanan Yehezkel, Boaz Lerner","year":"2009","venue":"Journal of Machine Learning Research","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}