[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-120641-en":3,"doc-seo-120641-105":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},120641,7971461741311,"Ophelia","https://ap-avatar.wpscdn.com/avatar/74000253aff267980c6?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779345379180704826",8,"Research & Report","Bayesian Inference and Optimal Design for the Sparse Linear Model - Academic paper overview","The linear model with a sparsity-favouring prior enables important applications across machine learning and signal processing, yet many approaches focus on MAP sparse estimates while ignoring posterior uncertainty. This paper develops Bayesian optimal design (experiment planning) where uncertainty accuracy is essential. Expectation propagation approximate inference for the Laplace prior is used to analyze numerical stability and obtain a robust algorithm. Model hyperparameters are learned via empirical Bayes marginal likelihood maximisation, with ideas for scaling to large underdetermined problems. Results include gene regulatory network identification and sparse coding for natural images, supporting compressive sensing performance.","Bayesian Inference and Optimal Design for the Sparse Linear Model  \nMatthias W. Seeger SEEGER@TUEBINGEN . MPG . DE  \nMax Planck Institute for Biological Cybernetics Spemannstr. 38, Tbingen, Germany  \nEditor: Martin Wainwright  \nAbstract  \nThe linear model with sparsity-favouring prior on the coefficients has important applications in many different domains. In machine learning, most methods to date search for maximum a posteriori sparse solutions and neglect to represent posterior uncertainties. In this paper, we address problems of Bayesian optimal design (or experiment planning), for which accurate estimates of uncertainty are essential. To this end, we employ expectation propagation approximate inference for the linear model with Laplace prior, giving new insight into numerical stability properties and proposing a robust algorithm. We also show how to estimate model hyperparameters by empirical Bayesian maximisation of the marginal likelihood, and propose ideas in order to scale up the method to very large underdetermined problems.  \nWe demonstrate the versatility of our framework on the application of gene regulatory network identification from micro-array expression data, where both the Laplace prior and the active experimental design approach are shown to result in significant improvements. We also address the problem of sparse coding of natural images, and show how our framework can be used for compressive sensing tasks.  \nPart of this work appeared in Seeger et al. (2007b) . The gene network identification application appears in Steinke et al. (2007) .  \nKeywords: sparse linear model, Laplace prior, expectation propagation, approximate inference, optimal design, Bayesian statistics, gene network recovery, image coding, compressive sensing  \n1. Introduction  \nIn many settings favoured in current machine learning work, the model and data set are given in advance, and predictions with low error are sought. Many methods from different paradigms have successfully been applied to these problems. While Bayesian approaches, such as the one we describe here, enjoy some benefits in this regime, they can be more difficult to implement, less algorithmically robust, and often require more computation time than, for example, penalised estimation methods, whose computation often reduces to a standard optimisation problem. In our opinion, the real practical power of the Bayesian way is revealed better in higher-level tasks such as making optimally cost-efficient decisions or experimental design. In the latter, aspects of the model and measurement experiments are adapted based on growing knowledge about the current situation, and data is sampled in a sequential and actively controlled manner, with the aim of obtaining answers as quickly as possible. Our main motivation in the present work is to demonstrate how Bayesian experimental design can be implemented in a computationally efficient and robust way, and how a range of challenging applications can benefit from selectively sampling data where it is most needed.  \n􀀍c2008 Matthias Seeger.  \nSEEGER  \nA number of characteristics of the framework we propose here, are especially useful, if not essential, to drive efficient experimental design for the applications we consider. The latter, at least in the sequential variant discussed here, proceeds through a significant number of individual decisions (say, where to sample data next) . In order to make each decision, our current uncertainty in variables of interest needs to be estimated quantitatively, and for a large number of candidates we have to consider how, and by how much, each of them would reduce this uncertainty estimate. As will become clear in the sequel, the uncertainty estimate is given by the posterior distribution, an approximation to which can be obtained robustly and efficiently by our method. The estimate is given as a Gaussian distribution, whose change after one more experiment can robustly and very efficiently be quantified. These poi","cbCaivFvhbeCS2SP","https://ap.wps.com/l/cbCaivFvhbeCS2SP","pdf",779523,1,55,"English","en",105,"# Introduction\n## Bayesian approach and experimental design motivation\n## Sparse linear model and underdetermined settings\n## Bayesian priors for sparsity\n## Posterior uncertainty estimation via expectation propagation","[{\"question\":\"What gap does the paper address in sparse Bayesian modeling?\",\"answer\":\"It targets Bayesian optimal design where representing posterior uncertainty is crucial, rather than relying only on MAP sparse solutions that neglect uncertainty.\"},{\"question\":\"How does the method approximate inference in the sparse linear model?\",\"answer\":\"It uses expectation propagation approximate inference for the linear model with a Laplace prior, yielding insight into numerical stability and a robust algorithm.\"},{\"question\":\"Which applications demonstrate the framework’s usefulness?\",\"answer\":\"Gene regulatory network identification from micro-array data and sparse coding of natural images, including connections to compressive sensing tasks.\"}]","Bayesian Inference and Optimal Design for the Sparse Linear Model - Academic paper overview | PDF",1785731049,139,{"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},"bayesian-inference-and-optimal-design-for-the-sparse-linear-model-academic-paper-overview","",{"@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/bayesian-inference-and-optimal-design-for-the-sparse-linear-model-academic-paper-overview/120641/",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","2026-08-03",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 gap does the paper address in sparse Bayesian modeling?","Question",{"text":75,"@type":76},"It targets Bayesian optimal design where representing posterior uncertainty is crucial, rather than relying only on MAP sparse solutions that neglect uncertainty.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the method approximate inference in the sparse linear model?",{"text":80,"@type":76},"It uses expectation propagation approximate inference for the linear model with a Laplace prior, yielding insight into numerical stability and a robust algorithm.",{"name":82,"@type":73,"acceptedAnswer":83},"Which applications demonstrate the framework’s usefulness?",{"text":84,"@type":76},"Gene regulatory network identification from micro-array data and sparse coding of natural images, including connections to compressive sensing tasks.","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"]