{"acknowledgement":"This work was initiated at the Second Bellairs Workshop on Causality held at the Bellairs Research Institute, January 6–13, 2022; we thank all workshop participants for providing a stimulating research environment. The research of DX and SM was supported by the Air Force Office of Scientific Research under award number FA8655-22-1-7155. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the United States Air Force. We also thank SURF for the support in using the Dutch National Supercomputer Snellius. DY was supported by an Amazon fellowship and the International Max Planck Research School for Intelligent Systems (IMPRS-IS). Work done outside of Amazon. SL was supported by an IVADO excellence PhD scholarship and by Samsung Electronics Co., Ldt. JvK acknowledges support from the German Federal Ministry of Education and Research (BMBF)\r\nthrough the Tübingen AI Center (FKZ: 01IS18039B).\r\n","department":[{"_id":"FrLo"}],"article_processing_charge":"No","citation":{"apa":"Xu, D., Yao, D., Lachapelle, S., Taslakian, P., von Kügelgen, J., Locatello, F., &#38; Magliacane, S. (2023). A sparsity principle for partially observable causal representation learning. In <i>Causal Representation Learning Workshop at NeurIPS 2023</i>. New Orleans, LA, United States: OpenReview.","chicago":"Xu, Danru, Dingling Yao, Sebastien Lachapelle, Perouz Taslakian, Julius von Kügelgen, Francesco Locatello, and Sara Magliacane. “A Sparsity Principle for Partially Observable Causal Representation Learning.” In <i>Causal Representation Learning Workshop at NeurIPS 2023</i>. OpenReview, 2023.","ista":"Xu D, Yao D, Lachapelle S, Taslakian P, von Kügelgen J, Locatello F, Magliacane S. 2023. A sparsity principle for partially observable causal representation learning. Causal Representation Learning Workshop at NeurIPS 2023. CRL: Causal Representation Learning Workshop at NeurIPS, 54.","ieee":"D. Xu <i>et al.</i>, “A sparsity principle for partially observable causal representation learning,” in <i>Causal Representation Learning Workshop at NeurIPS 2023</i>, New Orleans, LA, United States, 2023.","short":"D. Xu, D. Yao, S. Lachapelle, P. Taslakian, J. von Kügelgen, F. Locatello, S. Magliacane, in:, Causal Representation Learning Workshop at NeurIPS 2023, OpenReview, 2023.","ama":"Xu D, Yao D, Lachapelle S, et al. A sparsity principle for partially observable causal representation learning. In: <i>Causal Representation Learning Workshop at NeurIPS 2023</i>. OpenReview; 2023.","mla":"Xu, Danru, et al. “A Sparsity Principle for Partially Observable Causal Representation Learning.” <i>Causal Representation Learning Workshop at NeurIPS 2023</i>, 54, OpenReview, 2023."},"month":"12","date_created":"2024-02-07T15:17:51Z","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ddc":["000"],"oa":1,"file_date_updated":"2024-02-13T08:50:53Z","date_updated":"2024-02-13T08:59:27Z","has_accepted_license":"1","type":"conference","_id":"14958","author":[{"last_name":"Xu","full_name":"Xu, Danru","first_name":"Danru"},{"first_name":"Dingling","full_name":"Yao, Dingling","last_name":"Yao","id":"d3e02e50-48a8-11ee-8f62-c108061797fa"},{"last_name":"Lachapelle","first_name":"Sebastien","full_name":"Lachapelle, Sebastien"},{"last_name":"Taslakian","full_name":"Taslakian, Perouz","first_name":"Perouz"},{"first_name":"Julius","full_name":"von Kügelgen, Julius","last_name":"von Kügelgen"},{"last_name":"Locatello","id":"26cfd52f-2483-11ee-8040-88983bcc06d4","first_name":"Francesco","full_name":"Locatello, Francesco","orcid":"0000-0002-4850-0683"},{"last_name":"Magliacane","full_name":"Magliacane, Sara","first_name":"Sara"}],"conference":{"end_date":"2023-12-15","start_date":"2023-12-15","name":"CRL: Causal Representation Learning Workshop at NeurIPS","location":"New Orleans, LA, United States"},"publication_status":"published","publication":"Causal Representation Learning Workshop at NeurIPS 2023","abstract":[{"text":"Causal representation learning (CRL) aims at identifying high-level causal variables from low-level data, e.g. images. Current methods usually assume that all causal variables are captured in the high-dimensional observations. In this work, we focus on learning causal representations from data under partial observability, i.e., when some of the causal variables are not observed in the measurements, and the set of masked variables changes across the different samples. We introduce some initial theoretical results for identifying causal variables under partial observability by exploiting a sparsity regularizer, focusing in particular on the linear and piecewise linear mixing function case. We provide a theorem that allows us to identify the causal variables up to permutation and element-wise linear transformations in the linear case and a lemma that allows us to identify causal variables up to linear transformation in the piecewise case. Finally, we provide a conjecture that would allow us to identify the causal variables up to permutation and element-wise linear transformations also in the piecewise linear case. We test the theorem and conjecture on simulated data, showing the effectiveness of our method.","lang":"eng"}],"article_number":"54","publisher":"OpenReview","year":"2023","day":"05","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"date_published":"2023-12-05T00:00:00Z","license":"https://creativecommons.org/licenses/by/4.0/","file":[{"content_type":"application/pdf","file_size":552357,"date_created":"2024-02-13T08:50:53Z","checksum":"484efc27bda75ed6666044989695d9b6","access_level":"open_access","relation":"main_file","file_name":"2023_CRL_Xu.pdf","success":1,"creator":"dernst","file_id":"14982","date_updated":"2024-02-13T08:50:53Z"}],"language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://openreview.net/forum?id=Whr6uobelR"}],"quality_controlled":"1","title":"A sparsity principle for partially observable causal representation learning","oa_version":"Published Version"}