[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-117205-en":3,"doc-seo-117205-105":30,"detail-sidebar-cat-0-en-105":91},{"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":4,"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},117205,5909877438554,"Maeve","https://ap-avatar.wpscdn.com/avatar/5600025385ad2bf12a7?_k=1778553567797529272",8,"Research & Report","Multiscale Causal Structure Learning","Causal structure learning methods extract causal relationships from observed data, yet prevailing approaches assume interactions only at the same sampling frequency as the data. This work introduces a multiscale learning method for linear causal graphs across different time scales. It models instantaneous and lagged relations between multiple time series at varying scales using wavelet transforms, enforcing sparsity and DAG constraints to maintain directed, acyclic causality. MS-CASTLE provides consistent results under diverse noise and wavelet choices, while its single-scale variant, SS-CASTLE, improves computational efficiency, performance, and robustness on synthetic data, and is applied to risk dynamics across global equity markets during COVID-19.","Multiscale Causal Structure Learning  \nGabriele D’Acunto  \nDIAG, Sapienza University of Rome Centai Institute, Turin, Italy  \nPaolo Di Lorenzo  \nDIET, Sapienza University of Rome  \nSergio Barbarossa  \nDIET, Sapienza University of Rome  \n[gabriele. dacunto@uniroma1.it](gabriele. dacunto@uniroma1.it)  \n[paolo. dilorenzo@uniroma1.it](paolo. dilorenzo@uniroma1.it)  \n[sergio. barbarossa@uniroma1.it](sergio. barbarossa@uniroma1.it)  \nReviewed on OpenReview: [https: // openreview. net/ forum? id= Ub6XILEF9x](https: // openreview. net/ forum? id= Ub6XILEF9x)  \nAbstract  \nCausal structure learning methods are vital for unveiling causal relationships embedded into observed data. However, the state of the art suffers a major limitation: it assumes that causal interactions occur only at the frequency at which data is observed. To address this limitation, this paper proposes a method that allows structural learning of linear causal relationships occurring at different time scales. Specifically, we explicitly take into account instantaneous and lagged inter-relations between multiple time series, represented at different scales, hinging on wavelet transform. We cast the problem as the learning of a multiscale causal graph having sparse structure and dagness constraints, enforcing causality through directed and acyclic topology. To solve the resulting (non-convex) formulation, we propose an algorithm termed MS-CASTLE, which exhibits consistent performance across different noise distributions and wavelet choices. We also propose a single-scale version of our algorithm, SS-CASTLE, which outperforms existing methods in computational efficiency, performance, and robustness on synthetic data. Finally, we apply the proposed approach to learn the multiscale causal structure of the risk of 15 global equity markets, during covid-19  \npandemic, illustrating the importance of multiscale analysis to reveal useful interactions at different time resolutions. Financial investors can leverage our approach to manage risk within equity portfolios from a causal perspective, tailored to their investment horizon.  \n1 Introduction  \nThe study of causal relationships plays a fundamental role in our understanding of complex systems. However, learning causal relationships is a challenging task, and often is not even possible to directly act on the systems of interest (e.g., social networks) because of ethics, feasibility, or cost issues. Thus, the ability to unravel causal structures from the observed data, also known as causal structure learning, is an attractive technology that has received growing attention in the last years, also thanks to the ever-increasing volume of available data, see e.g., (Pearl, 2009; Peters et al., 2017; Glymour et al., 2019; Schölkopf et al., 2021) . In the literature, several works hinged on directed acyclic graphs (DAGs) to represent causal dependencies (i.e., directed edges) between the constituents (e.g., nodes) of the considered system (Vowels et al., 2022) . Indeed, the acyclicity requirement represents a necessary condition in order to set causes apart from effects; a result that cannot be accomplished in the presence of feedback loops among the nodes. In case the nodes of the DAG are associated with time series observations, the dependencies represented by the DAG refer to causal interactions occurring between the values of the time series within the same timestamp and across  \ndifferent time stamps. The formers are called instantaneous, whereas the latters, since we can only observe causal interactions coming from the past, are named lagged.  \nRelated works. Causal structure learning algorithms can be classified in accordance with the approach used to infer the associated DAG. In particular, we can identify three main different classes: (i) constraintbased approaches, which run conditional independence tests to validate the presence of an edge between two variables (Spirtes et al., 2000; Huang et al., 2020); (ii) score-based me","cbCaigpWQqiyNt35","https://ap.wps.com/l/cbCaigpWQqiyNt35","pdf",1777867,1,39,"English","en",105,"# Introduction\n## Related works\n## Time-series causal inference background\n## Problem formulation and approach outline\n## Proposed methods: MS-CASTLE and SS-CASTLE","[{\"question\":\"What limitation of existing causal structure learning methods does this paper address?\",\"answer\":\"It addresses the assumption that causal interactions occur only at the observed data frequency.\"},{\"question\":\"How does the proposed approach model relationships across different time scales?\",\"answer\":\"It explicitly represents instantaneous and lagged inter-relations between multiple time series at different scales using wavelet transforms.\"},{\"question\":\"What are MS-CASTLE and SS-CASTLE, and how do they differ?\",\"answer\":\"MS-CASTLE learns multiscale causal structure with sparse and DAG constraints, while SS-CASTLE is a single-scale version designed to improve computational efficiency, performance, and robustness on synthetic data.\"}]","Multiscale Causal Structure Learning | PDF",1785674405,98,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"multiscale-causal-structure-learning","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/multiscale-causal-structure-learning/117205/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-02",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What limitation of existing causal structure learning methods does this paper address?","Question",{"text":75,"@type":76},"It addresses the assumption that causal interactions occur only at the observed data frequency.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the proposed approach model relationships across different time scales?",{"text":80,"@type":76},"It explicitly represents instantaneous and lagged inter-relations between multiple time series at different scales using wavelet transforms.",{"name":82,"@type":73,"acceptedAnswer":83},"What are MS-CASTLE and SS-CASTLE, and how do they differ?",{"text":84,"@type":76},"MS-CASTLE learns multiscale causal structure with sparse and DAG constraints, while SS-CASTLE is a single-scale version designed to improve computational efficiency, performance, and robustness on synthetic data.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]