[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-120551-en":3,"doc-seo-120551-105":30,"detail-sidebar-cat-0-en-105":92},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},120551,687197207919,"Theodora","https://ap-avatar.wpscdn.com/avatar/a000253d6f5f7c60be?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779446848396160552",8,"Research & Report","Invariance & Causal Representation Learning - Prospects and Limitations","Learning causal representations without assumptions is fundamentally impossible, which motivates the need for carefully chosen inductive biases. Invariance of causal mechanisms offers a promising route for tackling out-of-distribution prediction. This work examines invariance as a candidate assumption to enable identifiability of causal representations. It proves that invariance alone cannot identify latent causal variables. Building on these impossibility results and practical considerations, it revisits the standard identifiability goal and suggests directions for adaptation.","Invariance & Causal Representation Learning: Prospects and Limitations  \nSimon Bing [bing@campus.tu-berlin. de](bing@campus.tu-berlin. de)  \nTechnische Universität Berlin  \nTom Hochsprung  \nGerman Aerospace Center (DLR), Institute of Data Science Technische Universität Berlin  \nJonas Wahl  \nTechnische Universität Berlin  \nGerman Aerospace Center (DLR), Institute of Data Science  \nUrmi Ninad  \nTechnische Universität Berlin  \nGerman Aerospace Center (DLR), Institute of Data Science  \nJakob Runge  \nScaDS. AI Dresden/Leipzig, TU Dresden  \nGerman Aerospace Center (DLR), Institute of Data Science Technische Universität Berlin  \nReviewed on OpenReview: [https: // openreview. net/ forum? id= lpOC6s4BcM](https: // openreview. net/ forum? id= lpOC6s4BcM)  \nAbstract  \nLearning causal representations without assumptions is known to be fundamentally impossible, thus establishing the need for suitable inductive biases. At the same time, the invariance of causal mechanisms has emerged as a promising principle to address the challenge of out-of-distribution prediction which machine learning models face. In this work, we explore this invariance principle as a candidate assumption to achieve identifiability of causal representations. While invariance has been utilized for inference in settings where the causal variables are observed, theoretical insights of this principle in the context of causal representation learning are largely missing. We assay the connection between invariance and causal representation learning by establishing impossibility results which show that invariance alone is insufficient to identify latent causal variables. Together with practical considerations, we use our results to reflect generally on the commonly used notion of identifiability in causal representation learning and potential adaptations of this goal moving forward.  \n1 Introduction  \nInferring high-level causal variables from low-level measurements is a problem garnering increased attention in fields interested in understanding epiphenomena that cannot be directly measured and where controlled experiments are not possible due to practical, economical or ethical considerations, for instance in healthcare (Johansson et al. , 2022), biology (Lopez et al. , 2023) or climate science (Tibau et al. , 2022) . This problem of causal representation learning (Schölkopf et al. , 2021) has been shown to be fundamentally underconstrained (Locatello et al. , 2019), leading to various approaches exploring which assumptions lead to algorithms that identify the latent causal variables.  \nRecent works either restrict the underlying causal model (Buchholz et al. , 2024 ; Lachapelle et al. , 2024), the transformation causal variables undergo (Ahuja et al. , 2023 ; Lachapelle et al. , 2023), or both (Squires et al. , 2023) . They include interventional or counterfactual data (Ahuja et al. , 2023 ; Zhang et al. , 2023 ; Squireset al. , 2023 ; Buchholz et al. , 2024 ; Bing et al. , 2024 ; Brehmer et al. , 2022), use supervisory signals such as time structure (Hyvärinen & Morioka, 2017 ; Hälvä & Hyvärinen, 2020 ; Yao et al. , 2021) or knowledge of intervention targets (Lippe et al. , 2022b;a) .  \nWe explore another type of inductive bias for achieving identifiability of causal representations, namely the invariance of causal mechanisms (Peters et al. , 2017) . First shown by Haavelmo (1944), causal variables lead to predictive models that are invariant under interventions, and since causal representation learning is tasked with recovering precisely these variables, we investigate if and to which degree the principle of invariance can be used as a signal to recover latent causal variables from observations.  \nWhile invariance has been used for causal inference (Peters et al. , 2016 ; Bühlmann, 2018 ; Meinshausen, 2018), none of these works considers the setting where we only have access to observations that are related to the underlying causal variables by some unknown transformation.","cbCailQGrsuKQqrr","https://ap.wps.com/l/cbCailQGrsuKQqrr","pdf",406568,1,16,"English","en",105,"# Introduction\n# Problem setting","[{\"question\":\"Why is learning causal representations without assumptions impossible?\",\"answer\":\"The document states that identifying causal representations requires inductive biases because the problem is fundamentally underconstrained.\"},{\"question\":\"How does invariance of causal mechanisms relate to causal representation learning?\",\"answer\":\"It treats invariance as an assumption signal, aiming to recover the latent variables whose causal mechanisms remain invariant under interventions.\"},{\"question\":\"What do the paper’s impossibility results show?\",\"answer\":\"They show that invariance alone is insufficient to identify latent causal variables when only transformed observations are available.\"}]","Invariance & Causal Representation Learning - 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