[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-665616-105":59,"doc-detail-665616-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","join-graph-decomposition-bounds-for-influence-diagrams-research-paper","Join Graph Decomposition Bounds for Influence Diagrams - Research Paper","","We introduce a direct decomposition method for bounding the maximum expected utility (MEU) in influence diagrams, targeting the bottleneck of model-size explosion seen in reduction-to-Marginal-Map approaches over Bayesian networks. The method extends earlier decomposition principles from probabilistic inference using valuation algebra, capturing multiplicative and additive local structures inherent in influence diagrams. Experiments on four benchmarks show clear gains, producing tighter upper bounds on MEU than reduction-based baselines and demonstrating the effectiveness of the approach.",{"@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/join-graph-decomposition-bounds-for-influence-diagrams-research-paper/665616/",{"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/join-graph-decomposition-bounds-for-influence-diagrams-research-paper/665616.png","ImageObject",300,407,{"name":92,"@type":93},"Asher","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-29",true,{"@type":102,"interactionType":103,"userInteractionCount":81},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the main goal of the proposed method for influence diagrams?","Question",{"text":112,"@type":113},"The method focuses on computing an upper bound on the maximum expected utility (MEU) for sequential decision-making under uncertainty in influence diagrams.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"Why does the paper avoid reduction-based approaches to Marginal Map?",{"text":117,"@type":113},"Reduction to Marginal Map over Bayesian networks can cause a large explosion in model size; the proposed approach aims to compute bounds directly to avoid that issue.",{"name":119,"@type":110,"acceptedAnswer":120},"What is the key technical framework enabling decomposition in the paper?",{"text":121,"@type":113},"The approach uses valuation algebra to represent and exploit both multiplicative and additive local structures present in influence diagrams, supporting the join graph decomposition bounds.","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},665616,1793305248,{"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":81,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":52,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":129,"read_time":143},687197207639,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Join Graph Decomposition Bounds for Influence Diagrams  \nJunkyu Lee Alexander Ihler Rina Dechter  \nDonald Bren School of Information and Computer Sciences University of California, Irvine {junkyul, ihler, [dechter} @ics.uci.edu](dechter} @ics.uci.edu)  \nAbstract  \nWe introduce a new decomposition method for bounding the maximum expected utility of influence diagrams. While most current schemes use reductions to the Marginal Map task over a Bayesian Network, our approach is direct, aiming to avoid the large explosion in the model size that often results by such reductions. In this paper, we extend to influence diagrams the principles of decomposition methods that were applied earlier to probabilistic inference, utilizing an algebraic framework called valuation algebra which effectively captures both multiplicative and additive local structures present in influence diagrams. Empirical evaluation on four benchmarks demonstrates the effectiveness of our approach compared to reduction-based approaches and illustrates significant improvements in the upper bounds on maximum expected utility.  \n1 INTRODUCTION  \nAn influence diagram (ID)[Howard and Matheson, 2005] is a graphical model for sequential decision-making under uncertainty that compactly captures the local structure of the conditional independence of probability functions and the additivity of utility functions. Its structure is captured by a directed acyclic graph (DAG) over nodes representing the variables (decision and chance variables) . The standard query on an ID is finding the maximum expected utility (MEU) and an optimal policy, at each decision subject to the history of observations and decisions. Our focus is on computing an upper bound on the MEU in a single agent sequential decision-making scenario when we assume perfect recall. The computation of upper bounds is desirable not only because exact computation is exponential in the number of variables appearing  \nin the history, but also because it can be used as a building block of algorithmic frameworks such as heuristic search and sampling.  \nEarlier work. One early work that yields bounds on many inference tasks in an anytime manner is the minibucket elimination (MBE) scheme that provides upper and lower bounds of graphical model queries by enforcing problem decomposition during the variable elimination process [Dechter and Rish, 2003] . In particular, Dechter [2000] presented an MBE algorithm for influence diagrams. A different principle for generating bounds on the MEU is to relax the constraints imposed on the information available at each stage and for each decision (thus making more observations visible to each decision) . This information relaxation scheme relaxes the constraints imposed on the information available at each stage and it also permits variable reordering during processing [Nilsson and Hohle, 2001] . In particular, Yuan et al. [2010] presented an AND/OR depth-first branch and bound search algorithm guided by upper bounds generated by such flexible variable orderings.  \nAn alternative set of schemes exploit translations between the maximum a posteriori inference (MMAP) in a Bayesian network (BN) and the MEU inference in an ID [Mauá, 2016] . The idea is to compute the upper bound of the MMAP of the BN translated from an input ID. However, the number of auxiliary variables introduced by the translation is exponential in the size of the history under the perfect recall assumption. If all utility functions were multiplicative, an ID could be treated as an unnormalized distribution and MMAP inference would be applied directly. Liu and Ihler [2012] presented a variational formulation for computing the MEU and message passing algorithms for such IDs where the additive utilities are converted into multiplicative utilities by introducing a latent selector variable. However, such a translation can make it difficult to exploit decompositions present in the additive utility functions.  \nContributions. We develop a de","cbCaicDt0XzVL7Ci","https://ap.wps.com/l/cbCaicDt0XzVL7Ci","pdf",684778,"English","# Abstract\n# 1 Introduction\n# 2 Preliminaries\n## 2.1 Influence Diagrams","[{\"question\":\"What is the main goal of the proposed method for influence diagrams?\",\"answer\":\"The method focuses on computing an upper bound on the maximum expected utility (MEU) for sequential decision-making under uncertainty in influence diagrams.\"},{\"question\":\"Why does the paper avoid reduction-based approaches to Marginal Map?\",\"answer\":\"Reduction to Marginal Map over Bayesian networks can cause a large explosion in model size; the proposed approach aims to compute bounds directly to avoid that issue.\"},{\"question\":\"What is the key technical framework enabling decomposition in the paper?\",\"answer\":\"The approach uses valuation algebra to represent and exploit both multiplicative and additive local structures present in influence diagrams, supporting the join graph decomposition bounds.\"}]","Join Graph Decomposition Bounds for Influence Diagrams - Research Paper | PDF",25]