{"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/towards-a-learning-theory-of-cause-effect","title":"Towards a Learning Theory of Cause-Effect Inference","arxiv_id":"1502.02398","date":"2015-02-09","proceeding":null,"authors":["David Lopez-Paz","Krikamol Muandet","Bernhard Schölkopf","Ilya Tolstikhin"],"abstract":"We pose causal inference as the problem of learning to classify probability\ndistributions. In particular, we assume access to a collection\n$\\{(S_i,l_i)\\}_{i=1}^n$, where each $S_i$ is a sample drawn from the\nprobability distribution of $X_i \\times Y_i$, and $l_i$ is a binary label\nindicating whether \"$X_i \\to Y_i$\" or \"$X_i \\leftarrow Y_i$\". Given these data,\nwe build a causal inference rule in two steps. First, we featurize each $S_i$\nusing the kernel mean embedding associated with some characteristic kernel.\nSecond, we train a binary classifier on such embeddings to distinguish between\ncausal directions. We present generalization bounds showing the statistical\nconsistency and learning rates of the proposed approach, and provide a simple\nimplementation that achieves state-of-the-art cause-effect inference.\nFurthermore, we extend our ideas to infer causal relationships between more\nthan two variables.","url_abs":"http://arxiv.org/abs/1502.02398v2","url_pdf":"http://arxiv.org/pdf/1502.02398v2.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":"towards-a-learning-theory-of-cause-effect","repo_url":"https://github.com/lopezpaz/causation_learning_theory","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"causal-inference","task_name":"Causal Inference"},{"task_slug":"generalization-bounds","task_name":"Generalization Bounds"},{"task_slug":"learning-theory","task_name":"Learning Theory"}],"methods":[{"method_slug":"causal-inference","method_name":"Causal inference"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}