{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/bayesian-sparse-tucker-models-for-dimension","title":"Bayesian Sparse Tucker Models for Dimension Reduction and Tensor Completion","arxiv_id":"1505.02343","date":"2015-05-10","proceeding":null,"authors":["Qibin Zhao","Liqing Zhang","Andrzej Cichocki"],"abstract":"Tucker decomposition is the cornerstone of modern machine learning on\ntensorial data analysis, which have attracted considerable attention for\nmultiway feature extraction, compressive sensing, and tensor completion. The\nmost challenging problem is related to determination of model complexity (i.e.,\nmultilinear rank), especially when noise and missing data are present. In\naddition, existing methods cannot take into account uncertainty information of\nlatent factors, resulting in low generalization performance. To address these\nissues, we present a class of probabilistic generative Tucker models for tensor\ndecomposition and completion with structural sparsity over multilinear latent\nspace. To exploit structural sparse modeling, we introduce two group sparsity\ninducing priors by hierarchial representation of Laplace and Student-t\ndistributions, which facilitates fully posterior inference. For model learning,\nwe derived variational Bayesian inferences over all model (hyper)parameters,\nand developed efficient and scalable algorithms based on multilinear\noperations. Our methods can automatically adapt model complexity and infer an\noptimal multilinear rank by the principle of maximum lower bound of model\nevidence. Experimental results and comparisons on synthetic, chemometrics and\nneuroimaging data demonstrate remarkable performance of our models for\nrecovering ground-truth of multilinear rank and missing entries.","url_abs":"http://arxiv.org/abs/1505.02343v1","url_pdf":"http://arxiv.org/pdf/1505.02343v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"bayesian-sparse-tucker-models-for-dimension","repo_url":"https://github.com/lijunsun/bgcp_imputation","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"compressive-sensing","task_name":"Compressive Sensing"},{"task_slug":"dimensionality-reduction","task_name":"Dimensionality Reduction"},{"task_slug":"tensor-decomposition","task_name":"Tensor Decomposition"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}