[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-291221-105":59,"doc-detail-291221-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","score-matching-enables-causal-discovery-of-nonlinear-additive-noise-models","Score Matching Enables Causal Discovery of Nonlinear Additive Noise Models","","This paper demonstrates how to recover causal graphs from the score of the data distribution in nonlinear additive (Gaussian) noise models. By using score matching algorithms as a core component, the work designs scalable causal discovery methods and introduces an efficient procedure to approximate the Jacobian of the score. Experiments show that the resulting SCORE algorithm is competitive with state-of-the-art causal discovery approaches while running significantly faster.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/score-matching-enables-causal-discovery-of-nonlinear-additive-noise-models/291221/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/score-matching-enables-causal-discovery-of-nonlinear-additive-noise-models/291221.png","ImageObject",300,407,{"name":92,"@type":93},"Ophelia","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-20","2026-09-17",true,{"@type":102,"interactionType":103,"userInteractionCount":44},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How does the method recover causal graphs in nonlinear additive noise models?","Question",{"text":112,"@type":113},"It uses the score of the data distribution, derived through score matching, to estimate the causal structure. Leaf identification and removal yield a complete topological order, after which classical pruning recovers the final graph.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"Why is causal discovery from observational data considered ill-posed?",{"text":117,"@type":113},"Different generative models with distinct causal structures can produce the same data distribution. Additional assumptions—such as additive noise—are needed to make the problem identifiable.",{"name":119,"@type":110,"acceptedAnswer":120},"What is the key advantage of the proposed SCORE algorithm?",{"text":121,"@type":113},"Empirically, SCORE matches the performance of leading causal discovery methods while being significantly faster due to scalable approximations, including an efficient score Jacobian approximation.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},291221,1789643779,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":44,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":129,"read_time":144,"preview_page_count":4},7971461741311,"https://ap-avatar.wpscdn.com/avatar/74000253aff267980c6?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779345379180704826","Score Matching Enables Causal Discovery of Nonlinear Additive Noise Models  \nPaul Rolland 1 Volkan Cevher 1 Matthus Kleindessner 2 Chris Russel 2 Bernhard Schlkopf 2  \nDominik Janzing 2 Francesco Locatello 2  \nAbstract  \nThis paper demonstrates how to recover causal graphs from the score of the data distribution in non-linear additive (Gaussian) noise models.  \nUsing score matching algorithms as a building block, we show how to design a new generation of scalable causal discovery methods. To showcase our approach, we also propose a new efficient method for approximating the score's Jacobian, enabling to recover the causal graph.  \nEmpirically, we find that the new algorithm, called SCORE, is competitive with state-of-theart causal discovery methods while being significantly faster.  \n1. Introduction  \nIn this work, we focus on causal discovery from purely observational data, i.e., finding a causal Directed Acyclic Graph (DAG) underlying a given data set. This problem is at the core of causality, since knowledge of the causal graph support the prediction of the effect of interventions (Peters et al., 2017 ; Schlkopf et al., 2021) .  \nIn general, the problem of causal discovery from observational data is ill-posed: there may be several generative models with various causal structures that can produce the same data distribution. Therefore, in order to make the problem well-posed, we need to rely on extra assumptionson the generative process. A popular solution is to assume that the noise injected during the generation of each variable is additive (see equation (1)) . Under additional assumptions on the link functions, it has been shown that such model is identifiable from purely observational data (Peterset al., 2014) .  \nMany causal discovery algorithms maximize a suitable loss  \n1´Ecole Polytechnique Fdral de Lausanne, Lausanne, Switzerland 2Amazon, Tuebingen, Germany. Correspondence to: Paul Rolland \u003Cpaul.rolland@epfl.ch>, Francesco Locatello \u003Clo[catelf@amazon.com](catelf@amazon.com) > .  \nProceedings of the 39 th International Conference on Machine Learning, Baltimore, Maryland, USA, PMLR 162, 2022 . Copyright 2022 by the author(s) .  \nfunction over the set of (DAGs) . Unfortunately, solving such problem using classical loss functions is known to be NP-hard (Chickering, 1996) . Therefore, recent methods focused on heuristic approximations, e.g., by using agreedy approach (PC, FCI (Spirtes et al., 2000 ; Zhang, 2008), GES (Chickering, 2002), CAM (B¨uhlmann et al., 2014) and others (Teyssier & Koller, 2012 ; Larranaga et al., 1996 ; Singh & Valtorta, 1993 ; Cooper & Herskovits, 1992 ; Bouckaert, 1992)), by expressing the problem as a continuous non-convex optimization problem and applying first-order optimization methods (GraNDAG (Lachapelle et al., 2019), NOTEARS (Zheng et al., 2018)), or by using Reinforcement Learning methods (RL-BIC (Zhu et al., 2019), CORL (Wang et al., 2021)) .  \nThere are two distinct aspects that make the search over DAGs difficult: the size of the set of DAGs, which grows super-exponentially with the number of nodes, and theacyclicity constraint. In order to reduce the impact of these two difficulties, approaches called order-based methods (Teyssier & Koller, 2012) tackle the problem in two phases. First, they find a certain topological ordering of the nodes, such that a node in the ordering can be a parent only of the nodes appearing after it in the same ordering. Second, the graph is constructed respecting the topological ordering and pruning spurious edges, e.g., using sparse regression (B¨uhlmann et al., 2014) . While the first step still requires to solve a combinatorial problem, the set of permutations is much smaller than the set ofDAGs. Moreover, once a topological order is fixed, the acyclicity constraint is naturally enforced, making the pruning step easier to solve.  \nThe method that we propose is an order-based one, where the topological order is estimated based on an approximation of the score of the","cbCaimKFXH0eJTQC","https://ap.wps.com/l/cbCaimKFXH0eJTQC","pdf",302531,13,"English","# Introduction\n## Causal discovery from observational data\n## Challenges in searching over DAGs\n## Order-based methods and score-based ordering","[{\"question\":\"How does the method recover causal graphs in nonlinear additive noise models?\",\"answer\":\"It uses the score of the data distribution, derived through score matching, to estimate the causal structure. Leaf identification and removal yield a complete topological order, after which classical pruning recovers the final graph.\"},{\"question\":\"Why is causal discovery from observational data considered ill-posed?\",\"answer\":\"Different generative models with distinct causal structures can produce the same data distribution. Additional assumptions—such as additive noise—are needed to make the problem identifiable.\"},{\"question\":\"What is the key advantage of the proposed SCORE algorithm?\",\"answer\":\"Empirically, SCORE matches the performance of leading causal discovery methods while being significantly faster due to scalable approximations, including an efficient score Jacobian approximation.\"}]","Score Matching Enables Causal Discovery of Nonlinear Additive Noise Models | PDF",33]