{"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-cp-factorization-of-incomplete","title":"Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determination","arxiv_id":"1401.6497","date":"2014-01-25","proceeding":null,"authors":["Qibin Zhao","Liqing Zhang","Andrzej Cichocki"],"abstract":"CANDECOMP/PARAFAC (CP) tensor factorization of incomplete data is a powerful\ntechnique for tensor completion through explicitly capturing the multilinear\nlatent factors. The existing CP algorithms require the tensor rank to be\nmanually specified, however, the determination of tensor rank remains a\nchallenging problem especially for CP rank. In addition, existing approaches do\nnot take into account uncertainty information of latent factors, as well as\nmissing entries. To address these issues, we formulate CP factorization using a\nhierarchical probabilistic model and employ a fully Bayesian treatment by\nincorporating a sparsity-inducing prior over multiple latent factors and the\nappropriate hyperpriors over all hyperparameters, resulting in automatic rank\ndetermination. To learn the model, we develop an efficient deterministic\nBayesian inference algorithm, which scales linearly with data size. Our method\nis characterized as a tuning parameter-free approach, which can effectively\ninfer underlying multilinear factors with a low-rank constraint, while also\nproviding predictive distributions over missing entries. Extensive simulations\non synthetic data illustrate the intrinsic capability of our method to recover\nthe ground-truth of CP rank and prevent the overfitting problem, even when a\nlarge amount of entries are missing. Moreover, the results from real-world\napplications, including image inpainting and facial image synthesis,\ndemonstrate that our method outperforms state-of-the-art approaches for both\ntensor factorization and tensor completion in terms of predictive performance.","url_abs":"http://arxiv.org/abs/1401.6497v2","url_pdf":"http://arxiv.org/pdf/1401.6497v2.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-cp-factorization-of-incomplete","repo_url":"https://github.com/zhaoxile/reproducible-tensor-completion-state-of-the-art","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"bayesian-inference","task_name":"Bayesian Inference"},{"task_slug":"image-generation","task_name":"Image Generation"},{"task_slug":"image-inpainting","task_name":"Image Inpainting"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1401.6497","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}