{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,10]],"date-time":"2026-06-10T15:09:35Z","timestamp":1781104175595,"version":"3.54.1"},"reference-count":23,"publisher":"National Academy of Sciences","issue":"27","license":[{"start":{"date-parts":[[2017,1,5]],"date-time":"2017-01-05T00:00:00Z","timestamp":1483574400000},"content-version":"vor","delay-in-days":184,"URL":"http:\/\/www.pnas.org\/preview_site\/misc\/userlicense.xhtml"}],"funder":[{"name":"Google Europe","award":["Doctoral Fellowship in Causal Inference"],"award-info":[{"award-number":["Doctoral Fellowship in Causal Inference"]}]}],"content-domain":{"domain":["www.pnas.org"],"crossmark-restriction":true},"short-container-title":["Proc. Natl. Acad. Sci. U.S.A."],"published-print":{"date-parts":[[2016,7,5]]},"abstract":"<jats:p>We describe a method for removing the effect of confounders to reconstruct a latent quantity of interest. The method, referred to as \u201chalf-sibling regression,\u201d is inspired by recent work in causal inference using additive noise models. We provide a theoretical justification, discussing both independent and identically distributed as well as time series data, respectively, and illustrate the potential of the method in a challenging astronomy application.<\/jats:p>","DOI":"10.1073\/pnas.1511656113","type":"journal-article","created":{"date-parts":[[2016,7,5]],"date-time":"2016-07-05T14:11:32Z","timestamp":1467727892000},"page":"7391-7398","update-policy":"https:\/\/doi.org\/10.1073\/pnas.cm10313","source":"Crossref","is-referenced-by-count":48,"title":["Modeling confounding by half-sibling regression"],"prefix":"10.1073","volume":"113","author":[{"given":"Bernhard","family":"Sch\u00f6lkopf","sequence":"first","affiliation":[{"name":"Department of Empirical Inference, MPI for Intelligent Systems, Max Planck Institute for Intelligent Systems, 72076 Tuebingen, Germany;"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David W.","family":"Hogg","sequence":"additional","affiliation":[{"name":"Center for Cosmology and Particle Physics, New York University, New York, NY 10003"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dun","family":"Wang","sequence":"additional","affiliation":[{"name":"Center for Cosmology and Particle Physics, New York University, New York, NY 10003"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Daniel","family":"Foreman-Mackey","sequence":"additional","affiliation":[{"name":"Center for Cosmology and Particle Physics, New York University, New York, NY 10003"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dominik","family":"Janzing","sequence":"additional","affiliation":[{"name":"Department of Empirical Inference, MPI for Intelligent Systems, Max Planck Institute for Intelligent Systems, 72076 Tuebingen, Germany;"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Carl-Johann","family":"Simon-Gabriel","sequence":"additional","affiliation":[{"name":"Department of Empirical Inference, MPI for Intelligent Systems, Max Planck Institute for Intelligent Systems, 72076 Tuebingen, Germany;"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jonas","family":"Peters","sequence":"additional","affiliation":[{"name":"Department of Empirical Inference, MPI for Intelligent Systems, Max Planck Institute for Intelligent Systems, 72076 Tuebingen, Germany;"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"341","published-online":{"date-parts":[[2016,7,5]]},"reference":[{"key":"e_1_3_3_1_2","first-page":"1255","volume-title":"Proceedings of the 29th International Conference on Machine Learning (ICML)","author":"Sch\u00f6lkopf B","year":"2012","unstructured":"B Sch\u00f6lkopf, , On causal and anticausal learning. Proceedings of the 29th International Conference on Machine Learning (ICML), eds J Langford, J Pineau (Omnipress, New York), pp. 1255\u20131262 (2012)."},{"key":"e_1_3_3_2_2","volume-title":"Causality","author":"Pearl J","year":"2000","unstructured":"J Pearl Causality (Cambridge Univ Press, New York, 2000)."},{"key":"e_1_3_3_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-2748-9"},{"key":"e_1_3_3_4_2","doi-asserted-by":"publisher","DOI":"10.1093\/oxfordjournals.oep.a041889"},{"key":"e_1_3_3_5_2","volume-title":"Economics and Philosophy","author":"Hoover KD","year":"2008","unstructured":"KD Hoover, Causality in economics and econometrics. Economics and Philosophy, eds SN Durlauf, LE Blume (Palgrave Macmillan, 2nd Ed, New York) Vol 6 (2008).","edition":"2"},{"key":"e_1_3_3_6_2","first-page":"2009","article-title":"Causal discovery with continuous additive noise models","volume":"15","author":"Peters J","year":"2014","unstructured":"J Peters, J Mooij, D Janzing, B Sch\u00f6lkopf, Causal discovery with continuous additive noise models. J Mach Learn Res 15(Jun), 2009\u20132053 (2014).","journal-title":"J Mach Learn Res"},{"key":"e_1_3_3_7_2","first-page":"689","volume-title":"Advances in Neural Information Processing Systems","author":"Hoyer P","year":"2009","unstructured":"P Hoyer, D Janzing, JM Mooij, J Peters, B Sch\u00f6lkopf, Nonlinear causal discovery with additive noise models. Advances in Neural Information Processing Systems, eds D Koller, D Schuurmans, Y Bengio, L Bottou (MIT Press, Cambridge, MA) Vol 21, 689\u2013696 (2009)."},{"key":"e_1_3_3_8_2","first-page":"2218","volume-title":"Proceedings of the 32nd International Conference on Machine Learning.","author":"Sch\u00f6lkopf B","year":"2015","unstructured":"B Sch\u00f6lkopf, , Removing systematic errors for exoplanet search via latent causes. Proceedings of the 32nd International Conference on Machine Learning., eds F Bach, D Blei (Microtome, Brookline, MA), pp. 2218\u20132226 (2015)."},{"key":"e_1_3_3_9_2","volume-title":"An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements","author":"Taylor JR","year":"1997","unstructured":"JR Taylor An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements (Univ Science Books, 2nd Ed, Herndon, VA, 1997).","edition":"2"},{"key":"e_1_3_3_10_2","doi-asserted-by":"publisher","DOI":"10.1038\/ng1847"},{"key":"e_1_3_3_11_2","doi-asserted-by":"publisher","DOI":"10.1038\/ng1702"},{"key":"e_1_3_3_12_2","doi-asserted-by":"publisher","DOI":"10.1093\/biostatistics\/kxj037"},{"key":"e_1_3_3_13_2","doi-asserted-by":"publisher","DOI":"10.1534\/genetics.108.094201"},{"key":"e_1_3_3_14_2","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1007\/978-3-540-78839-3_35","volume-title":"Research in Computational Molecular Biology: 12th Annual International Conference, RECOMB 2008","author":"Stegle O","year":"2008","unstructured":"O Stegle, A Kannan, R Durbin, JM Winn, Accounting for non-genetic factors improves the power of eQTL studies. Research in Computational Molecular Biology: 12th Annual International Conference, RECOMB 2008, eds M Vingron, L Wong (Springer, New York), pp. 411\u2013422 (2008)."},{"key":"e_1_3_3_15_2","doi-asserted-by":"publisher","DOI":"10.1093\/biostatistics\/kxr034"},{"key":"e_1_3_3_16_2","first-page":"249","volume-title":"25th Conference on Uncertainty in Artificial Intelligence","author":"Janzing D","year":"2009","unstructured":"D Janzing, J Peters, J Mooij, B Sch\u00f6lkopf, Identifying confounders using additive noise models. 25th Conference on Uncertainty in Artificial Intelligence, eds J Bilmes, AY Ng (AUAI Press, Corvallis, OR), pp. 249\u2013257 (2009)."},{"key":"e_1_3_3_17_2","doi-asserted-by":"publisher","DOI":"10.1086\/524677"},{"key":"e_1_3_3_18_2","doi-asserted-by":"publisher","DOI":"10.1086\/667698"},{"key":"e_1_3_3_19_2","doi-asserted-by":"publisher","DOI":"10.1086\/667697"},{"key":"e_1_3_3_20_2","doi-asserted-by":"publisher","DOI":"10.1088\/0004-637X\/806\/2\/215"},{"key":"e_1_3_3_21_2","doi-asserted-by":"publisher","DOI":"10.1086\/668847"},{"key":"e_1_3_3_22_2","doi-asserted-by":"publisher","DOI":"10.1093\/biostatistics\/kxv026"},{"key":"e_1_3_3_23_2","volume-title":"The Elements of Statistical Learning; Data Mining, Inference and Prediction","author":"Hastie T","year":"2009","unstructured":"T Hastie, R Tibshirani, J Friedman The Elements of Statistical Learning; Data Mining, Inference and Prediction (Springer, 2nd Ed, New York, 2009).","edition":"2"}],"container-title":["Proceedings of the National Academy of Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.pnas.org\/syndication\/doi\/10.1073\/pnas.1511656113","content-type":"unspecified","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pnas.org\/doi\/pdf\/10.1073\/pnas.1511656113","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,4,13]],"date-time":"2022-04-13T00:40:32Z","timestamp":1649810432000},"score":1,"resource":{"primary":{"URL":"https:\/\/pnas.org\/doi\/full\/10.1073\/pnas.1511656113"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,7,5]]},"references-count":23,"journal-issue":{"issue":"27","published-print":{"date-parts":[[2016,7,5]]}},"alternative-id":["10.1073\/pnas.1511656113"],"URL":"https:\/\/doi.org\/10.1073\/pnas.1511656113","relation":{},"ISSN":["0027-8424","1091-6490"],"issn-type":[{"value":"0027-8424","type":"print"},{"value":"1091-6490","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,7,5]]},"assertion":[{"value":"2016-07-05","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}