[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-153911-105":59,"doc-detail-153911-en":131},{"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":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","vector-gaussian-ceo-problem-under-logarithmic-loss-and-applications","Vector Gaussian CEO Problem Under Logarithmic Loss and Applications","","In this paper, the vector Gaussian Chief Executive Officer (CEO) problem is analyzed under a logarithmic loss distortion measure. K≥2 agents observe independently corrupted Gaussian versions of a remote vector Gaussian source and send rate-constrained messages to a decoder/CEO through noise-free links. The CEO also holds an additional Gaussian noisy observation and reconstructs the source within a target distortion level. An explicit characterization of the rate-distortion region is derived via a de Bruijn-identity-based outer bound using Fisher-information properties. Gaussian test channels with time-sharing achieve the optimal Berger–Tung inner bound, yielding complete solutions to related determinant-constraint quadratic CEO and distributed information bottleneck problems, plus Blahut–Arimoto-type numerical algorithms for both discrete and Gaussian models.",{"@graph":69,"@context":123},[70,84,106],{"@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/vector-gaussian-ceo-problem-under-logarithmic-loss-and-applications/153911/",{"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/vector-gaussian-ceo-problem-under-logarithmic-loss-and-applications/153911.png","ImageObject",300,407,{"name":92,"@type":93},"Margaret","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-27","2026-08-28",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",14,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What observations and communication setup define the vector Gaussian CEO problem?","Question",{"text":113,"@type":114},"K≥2 agents observe independently corrupted Gaussian versions of a remote vector Gaussian source and communicate separately with a central CEO/decoder over rate-constrained noise-free links. The CEO also has its own Gaussian noisy observation of the source.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How is distortion measured under the paper’s logarithmic loss criterion?",{"text":118,"@type":114},"Distortion uses a logarithmic loss penalty where each symbol contributes self-information loss based on the decoder’s assigned probability distribution for the observed outcome.",{"name":120,"@type":111,"acceptedAnswer":121},"What are the main theoretical and algorithmic contributions?",{"text":122,"@type":114},"The paper explicitly characterizes the rate-distortion region, shows Gaussian test channels with time-sharing exhaust the Berger–Tung inner bound, derives complete solutions to two related problems, and develops Blahut–Arimoto-type algorithms to compute the regions numerically for discrete and Gaussian settings.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},153911,1787884113,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":140,"language":141,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":67,"update_tm":130,"read_time":145,"preview_page_count":4},137451207643,"https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2","arXiv : 1811 .03933v2 [ cs .IT] 4 Feb 2020  \nVector Gaussian CEO Problem Under Logarithmic Loss and Applications  \nYi˘git U˘gur yz I˜naki Estella Aguerri y Abdellatif Zaidi yz  \ny Mathematical and Algorithmic Sciences Lab, Paris Research Center, Huawei Technologies,  \nBoulogne-Billancourt, 92100, France  \nz Universit Paris-Est, Champs-sur-Marne, 77454, France  \n[f](fyigit.ugur@gmail.com)[yigit.ugur@gmail.com](fyigit.ugur@gmail.com) , [inaki.estella@gmail.com](inaki.estella@gmail.com) , abdellatif.zaidi@u-pem.frg  \nAbstract  \nIn this paper, we study the vector Gaussian Chief Executive Officer (CEO) problem under logarithmic loss distortion measure. Specifically, K 􀀕 2 agents observe independently corrupted Gaussian noisy versions of a remote vector Gaussian source, and communicate independently with a decoder or CEO over rate-constrained noise-free links. The CEO also has its own Gaussian noisy observation of the source and wants to reconstruct the remote source to within some prescribed distortion level where the incurred distortion is measured under the logarithmic loss penalty criterion. We find an explicit characterization of the rate-distortion region of this model. The result can be seen as the counterpart to the vector Gaussian setting of that by Courtade-Weissman which provides the rate-distortion region of the model in the discrete memoryless setting. For the proof of this result, we obtain an outer bound by means of a technique that relies on the de Bruijn identity and the properties of Fisher information. The approach is similar to Ekrem-Ulukus outer bounding technique for the vector Gaussian CEO problem under quadratic distortion measure, for which it was there found generally non-tight; but it is shown here to yield a complete characterization of the region for the case of logarithmic loss measure. Also, we show that Gaussian test channels with time-sharing exhaust the Berger-Tung inner bound, which is optimal. Furthermore, application of our results allows us to find the complete solutions of two related problems: a quadratic vector Gaussian CEO problem with determinant constraint and the vector Gaussian distributed Information Bottleneck problem. Finally, we develop Blahut-Arimoto type algorithms that allow to compute numerically the regions provided in this paper, for both discrete and Gaussian models. With the known relevance of the logarithmic loss fidelity measure in the context of learning and prediction, the proposed algorithms may find usefulness in a variety of applications where learning is performed distributively. We illustrate the efficiency of our algorithms through some numerical examples.  \nThe results of this paper have been presented in part at the 2017 IEEE Information Theory Workshop [1] and in part at the 2018 IEEE Information Theory Workshop [2] .  \nXn  \nYn1  \nEncoder 1  \nR 1  \nEncoder 2  \nEncoder K  \n\n| R2  |\n| --- |\n| |\n|  |\n\n.  \n.  \n.  \nRK  \n\n| Yn2  |\n| --- |\n| YnK  |\n\nDecoder  \nYn0  \n^Xn  \nFig. 1: Chief Executive Officer (CEO) source coding problem with side information.  \nI. INTRODUCTION  \nConsider the vector Gaussian Chief Executive Officer (CEO) problem shown in Figure 1 . In this model, there are K 􀀕 2 agents each observing a noisy version of a vector Gaussian source X. The goal of the agents is to describe the source to a central unit, which wants to reconstruct this source to within a prescribed distortion level. The incurred distortion is measured according to some loss measure d : X 􀀂 ^X ! R, where ^X designates thereconstruction alphabet. For quadratic distortion measure, i.e.,  \nd (x; x^) = jx 􀀀 x^j 2 ;  \nthe rate-distortion region of the vector Gaussian CEO problem is still unknown in general, except in few special cases the most important of which is perhaps the case of scalar sources, i.e., scalar Gaussian CEO problem. For this case, a complete solution, in terms of characterization of the optimal rate-distortion region, was found independently by Oohama in [3] and by Prabhakaran et a","cbCaikN8oUO87hOO","https://ap.wps.com/l/cbCaikN8oUO87hOO","pdf",893968,38,"English","# Abstract\n# Introduction\n## Vector Gaussian CEO model and distortion measures\n## Logarithmic loss criterion and its role in soft reconstruction\n## Prior work and motivation for complete characterization","[{\"question\":\"What observations and communication setup define the vector Gaussian CEO problem?\",\"answer\":\"K≥2 agents observe independently corrupted Gaussian versions of a remote vector Gaussian source and communicate separately with a central CEO/decoder over rate-constrained noise-free links. The CEO also has its own Gaussian noisy observation of the source.\"},{\"question\":\"How is distortion measured under the paper’s logarithmic loss criterion?\",\"answer\":\"Distortion uses a logarithmic loss penalty where each symbol contributes self-information loss based on the decoder’s assigned probability distribution for the observed outcome.\"},{\"question\":\"What are the main theoretical and algorithmic contributions?\",\"answer\":\"The paper explicitly characterizes the rate-distortion region, shows Gaussian test channels with time-sharing exhaust the Berger–Tung inner bound, derives complete solutions to two related problems, and develops Blahut–Arimoto-type algorithms to compute the regions numerically for discrete and Gaussian settings.\"}]","Vector Gaussian CEO Problem Under Logarithmic Loss and Applications | PDF",96]