[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-128615-en":3,"doc-seo-128615-105":31,"detail-sidebar-cat-0-en-105":92},{"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":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":28,"seo_description":14,"update_tm":29,"read_time":30},128615,962084925502,"Lucas Martin","https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8",8,"Research & Report","Bayesian Inference for Sparse Generalized Linear Models","Framework for efficient, accurate approximate Bayesian inference in generalized linear models using expectation propagation. The approach supports factorizing priors that encode structured parameter assumptions such as sparsity or non-negativity, with emphasis on posterior log-concavity and its role in numerical stability and EP convergence. Experiments apply the method to a neuronal point-process spiking model from multiple electrodes, showing improved predictive performance when sparsity is enforced via a Laplace prior.","View metadata, citation and similar [papers at ](papers at core.ac.uk)[core.ac.uk](papers at core.ac.uk) brought to you by CORE  \nprovided by Infoscience- École polytechnique fédérale de Lausanne  \nBayesian Inference for Sparse Generalized Linear Models  \nMatthias Seeger, Sebastian Gerwinn, and Matthias Bethge  \nMax Planck Institute for Biological Cybernetics Spemannstr. 38, T􀁿ubingen, Germany  \nAbstract. We present a framework for e􀀎cient, accurate approximate Bayesian inference in generalized linear models (GLMs), based on the expectation propagation (EP) technique. The parameters can be endowed with a factorizing prior distribution, encoding properties such as sparsity or non-negativity. The central role of posterior log-concavity in Bayesian GLMs is emphasized and related to stability issues in EP. In particular, we use our technique to infer the parameters of a point process model for neuronal spiking data from multiple electrodes, demonstrating signi􀀌cantly superior predictive performance when a sparsity assumption is enforced via a Laplace prior distribution.  \n1 Introduction  \nThe framework of generalized linear models (GLM) [5] is a cornerstone of modern Statistics, o􀀋ering uni􀀌ed estimation and prediction methods for a large number of models frequently used in Machine Learning. In a Bayesian generalized linear model (B-GLM), assumptions about the model parameters (sparsity, nonnegativity, etc) are encoded in a prior distribution. For example, it is common to use an overparameterized model with many features together with a sparsity prior. Only such features relevant for describing the data will end up having signi􀀌cant weight under the Bayesian posterior. Importantly, for the models of interest in this paper, inference does not require combinatorial computational e􀀋orts, but can be done even with a large number of parameters.  \nExact Bayesian inference is not analytically tractable in most B-GLMs. In this paper, we show how to employ the expectation propagation (EP) technique for approximate inference in GLMs with factorizing prior distributions. We focus on models with log-concave (therefore unimodal) posterior, for which a careful EP implementation is numerically robust and tends to convergence rapidly to an accurate posterior approximation. The code used in our experiments will be made publicly available.  \nWe apply our technique to a point process model for neuronal spiking data from multiple electrodes. Here, each neuron is assumed to receive causal input from an external stimulus and the spike history, represented by features in a GLM. In the presence of high-dimensional stimuli (such as images), with many neurons recorded at a reasonable time resolution, we end up with a lot of features,  \nbut we can assume that the system can be described by a much smaller number of parameters. This calls for a sparsity prior, and we are able to con􀀌rm the importance of this prior assumption through our experiments, where our model achieves much better predictive performance with a Laplace sparsity prior than with a (traditionally favoured) Gaussian prior, especially for small to moderate sample sizes. Our model is inspired by [10], who identify commonly used spiking models as log-concave GLMs, but the Bayesian treatment as well as the usage of sparsity in this context is novel.  \nThe structure of the paper is as follows. In Section 2, we introduce and motivate the model class of B-GLMs. In Section 3, we show how the expectation propagation method can be applied to B-GLMs, motivating the central role of log-concavity in this context. Our multi-neuron spiking model is presented in Section 4, and experimental results are presented in Section 5 . We close with a discussion in Section 6 .  \n2 Bayesian Generalized Linear Models  \nThe models we are interested in here are speci􀀌ed in terms of primary parameters w (or weights) and hyperparameters 􀀒 . If D denotes the set of observations, the likelihood is P (Djw), and the (Bayesian) ","cbCailRoe2QnhuV5","https://ap.wps.com/l/cbCailRoe2QnhuV5","pdf",346020,2,1,12,"English","en",105,"# Introduction\n## Bayesian Generalized Linear Models\n# Approximate Inference with Expectation Propagation\n## Log-Concavity and Stability\n# Multi-Neuron Spiking Model\n## Experimental Results\n# Discussion","[{\"question\":\"What inference method does the paper use for Bayesian generalized linear models?\",\"answer\":\"It uses expectation propagation (EP) to perform efficient approximate Bayesian inference in GLMs with factorizing priors.\"},{\"question\":\"How are sparsity and non-negativity incorporated into the Bayesian model?\",\"answer\":\"They are encoded through factorizing prior distributions over parameters, such as Laplace priors for sparsity and constrained Gaussian or exponential priors for non-negativity.\"},{\"question\":\"Why is posterior log-concavity emphasized in the framework?\",\"answer\":\"The paper highlights that log-concavity (unimodality) supports a numerically robust EP implementation that tends to converge rapidly to an accurate approximation.\"}]","Bayesian Inference for Sparse Generalized Linear Models | PDF",1786002125,30,{"code":4,"msg":32,"data":33},"ok",{"site_id":25,"language":24,"slug":34,"title":13,"keywords":35,"description":14,"schema_data":36,"social_meta":87,"head_meta":89,"extra_data":91,"updated_unix":29},"bayesian-inference-for-sparse-generalized-linear-models","",{"@graph":37,"@context":86},[38,54,69],{"@type":39,"itemListElement":40},"BreadcrumbList",[41,45,48,51],{"item":42,"name":43,"@type":44,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":46,"name":47,"@type":44,"position":20},"https://docshare.wps.com/document/","Document",{"item":49,"name":12,"@type":44,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":44,"position":53},"https://docshare.wps.com/document/bayesian-inference-for-sparse-generalized-linear-models/128615/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":24,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":42,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-25","2026-08-06",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"What inference method does the paper use for Bayesian generalized linear models?","Question",{"text":76,"@type":77},"It uses expectation propagation (EP) to perform efficient approximate Bayesian inference in GLMs with factorizing priors.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"How are sparsity and non-negativity incorporated into the Bayesian model?",{"text":81,"@type":77},"They are encoded through factorizing prior distributions over parameters, such as Laplace priors for sparsity and constrained Gaussian or exponential priors for non-negativity.",{"name":83,"@type":74,"acceptedAnswer":84},"Why is posterior log-concavity emphasized in the framework?",{"text":85,"@type":77},"The paper highlights that log-concavity (unimodality) supports a numerically robust EP implementation that tends to converge rapidly to an accurate approximation.","https://schema.org",{"og:url":52,"og:type":88,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":90,"canonical":52},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":93},[94,98,102,106,111,116,121,123,128,131,135],{"id":21,"doc_module":4,"doc_module_name":47,"category_name":95,"show_sort_weight":96,"slug":97},"Story & Novel",90,"story-novel",{"id":20,"doc_module":4,"doc_module_name":47,"category_name":99,"show_sort_weight":100,"slug":101},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":47,"category_name":103,"show_sort_weight":104,"slug":105},"Exam",70,"exam",{"id":107,"doc_module":4,"doc_module_name":47,"category_name":108,"show_sort_weight":109,"slug":110},5,"Comic",60,"comic",{"id":112,"doc_module":4,"doc_module_name":47,"category_name":113,"show_sort_weight":114,"slug":115},6,"Technology",50,"technology",{"id":117,"doc_module":4,"doc_module_name":47,"category_name":118,"show_sort_weight":119,"slug":120},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":47,"category_name":12,"show_sort_weight":30,"slug":122},"research-report",{"id":124,"doc_module":4,"doc_module_name":47,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":47,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":47,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":47,"category_name":137,"show_sort_weight":107,"slug":138},19,"General","general"]