[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-128709-en":3,"doc-seo-128709-105":29,"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":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":11,"language":21,"language_code":22,"site_id":23,"html_lang":22,"table_of_contents":24,"faqs":25,"seo_title":26,"seo_description":14,"update_tm":27,"read_time":28},128709,962084926284,"Aurora","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Large Scale Variational Bayesian Inference for Structured Scale Mixture Models","Natural image statistics exhibit hierarchical dependencies across multiple scales. Modeling such prior knowledge in non-factorial latent tree models enhances performance for image denoising, inpainting, deconvolution, and reconstruction beyond standard factorial sparse priors. The work derives a large-scale approximate Bayesian inference method for generalized linear models with latent tree-structured scale mixture priors. Experiments on denoising and inpainting tasks show clear gains over MAP estimation and over inference using factorial priors.","CORE  Metadata, citation and similar [papers at core.ac.uk](papers at core.ac.uk)  \nProvided by Infoscience- École polytechnique fédérale de Lausanne  \nLarge Scale Variational Bayesian Inference for Structured Scale Mixture Models  \nYoung Jun Ko Matthias Seeger  \n[youngjun.ko@epfl.ch](youngjun.ko@epfl.ch)[ ](youngjun.ko@epfl.ch)[matthias.seeger@epfl.ch](matthias.seeger@epfl.ch)  \nSchool of Computer and Communication Sciences, Ecole Polytechnique F􀀓ed􀀓erale de Lausanne, Switzerland  \nAbstract  \nNatural image statistics exhibit hierarchical dependencies across multiple scales. Representing such prior knowledge in non-factorial latent tree models can boost performance of image denoising, inpainting, deconvolution or reconstruction substantially, beyond standard factorial \\sparse\" methodology. We derive a large scale approximate Bayesian inference algorithm for linear models with nonfactorial (latent tree-structured) scale mixture priors. Experimental results on a range of denoising and inpainting problems demonstrate substantially improved performance compared to MAP estimation or to inference with factorial priors.  \n1. Introduction  \nLeaps in performance have been realized for low-level computer vision problems, such as denoising, inpainting, deconvolution (debluring), image coding, undersampled reconstruction or acquisition optimization, by adopting super-Gaussian (\\sparse\") image priors. While most such methods employ simple factorial priors on single coe􀀎cients or groups, further substantial gains can be obtained by modelling higher-order dependencies via structured non-factorial prior distributions (Portilla et al. , 2003; Wipf & Nagarajan, 2008; Cevher et al. , 2010) . For example, representing the dependencies among multi-scale wavelet coe􀀎cients by a (latent) tree structure can boost accuracy for image compression and reconstruction (Crouse et al. , 1998; Papandreou et al. , 2008; He et al. , 2010) . However, previous approaches employing such non-factorial priors either run much slower than standard factorial methodology, or sacri􀀌ce performance by adopting  \nAppearing in Proceedings of the 29 th International Conference on Machine Learning, Edinburgh, Scotland, UK, 2012 . Copyright 2012 by the author(s)/owner(s) .  \nsuboptimal MAP estimation or naive mean 􀀌eld factorization assumptions, ignoring posterior covariance or uncertainty altogether in problems which are highly underdetermined.  \nIn this paper, we derive a large scale approximate Bayesian inference algorithm for generalized linear models with non-factorial (latent tree-structured) scale mixture priors. Our contributions are as follows:  \n􀀏 An image model with scale mixture prior on multi-scale wavelet coe􀀎cients, based on a latent discrete tree distribution. Mixture potentials can have arbitrary super-Gaussian components.  \n􀀏 A large scale double loop algorithm for Bayesian inference in these hybrid models. We do not require factorization assumptions between image pixels or wavelet coe􀀎cients. Our method is based on standard scalable technology (preconditioned conjugate gradients, penalized least squares) and can operate at the same scales as MAP estimation.  \n􀀏 An extension to incorporate non-log-concave potentials, such as Student's t, without sacri􀀌cing robustness of the optimization.  \n􀀏 Automatic Bayesian learning of a substantial number of hyperparameters from raw data. Folded into the variational optimization, this process does not require much overhead. It improves performance very signi􀀌cantly.  \n􀀏 An extensive evaluation on many inpainting and denoising datasets, comparing variational inference and MAP estimation for factorial and nonfactorial priors featuring di􀀋erent sparsity potentials.  \nOur 􀀌ndings suggest (a) that predicting the variational posterior mean strongly and consistently outperforms the popular posterior mode (MAP estimation), (b) that non-factorial priors tend to  \nboost performance compared to factorial ones, and (c) that Bayesian h","cbCaigbKJAwPeEUP","https://ap.wps.com/l/cbCaigbKJAwPeEUP","pdf",817518,1,"English","en",105,"# Introduction\n## Related Work\n# Method Overview\n## Image Model with Scale Mixture Prior\n## Large Scale Double Loop Bayesian Inference\n## Extension to Non-Log-Concave Potentials\n## Automatic Bayesian Hyperparameter Learning\n# Experimental Evaluation\n## Denoising Experiments\n## Inpainting Experiments\n# Conclusions","[{\"question\":\"What is the main contribution of the proposed method?\",\"answer\":\"It derives a large-scale approximate Bayesian inference algorithm for generalized linear models with non-factorial, latent tree-structured scale mixture priors.\"},{\"question\":\"How does the method use structured priors for image tasks?\",\"answer\":\"It models hierarchical multi-scale dependencies (e.g., wavelet coefficients) using a latent discrete tree distribution, enabling non-factorial prior structure.\"},{\"question\":\"How does the proposed Bayesian approach compare to MAP or factorial priors?\",\"answer\":\"Experiments on denoising and inpainting show substantially improved performance versus MAP estimation and versus inference using factorial priors.\"}]","Large Scale Variational Bayesian Inference for Structured Scale Mixture Models | 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is the main contribution of the proposed method?","Question",{"text":75,"@type":76},"It derives a large-scale approximate Bayesian inference algorithm for generalized linear models with non-factorial, latent tree-structured scale mixture priors.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the method use structured priors for image tasks?",{"text":80,"@type":76},"It models hierarchical multi-scale dependencies (e.g., wavelet coefficients) using a latent discrete tree distribution, enabling non-factorial prior structure.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the proposed Bayesian approach compare to MAP or factorial priors?",{"text":84,"@type":76},"Experiments on denoising and inpainting show substantially improved performance versus MAP estimation and versus inference using factorial 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