{"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/efficient-nonparametric-tensor-decomposition","title":"Efficient Nonparametric Tensor Decomposition for Binary and Count Data","arxiv_id":"2401.07711","date":"2024-01-15","proceeding":null,"authors":["Zerui Tao","Toshihisa Tanaka","Qibin Zhao"],"abstract":"In numerous applications, binary reactions or event counts are observed and stored within high-order tensors. Tensor decompositions (TDs) serve as a powerful tool to handle such high-dimensional and sparse data. However, many traditional TDs are explicitly or implicitly designed based on the Gaussian distribution, which is unsuitable for discrete data. Moreover, most TDs rely on predefined multi-linear structures, such as CP and Tucker formats. Therefore, they may not be effective enough to handle complex real-world datasets. To address these issues, we propose ENTED, an \\underline{E}fficient \\underline{N}onparametric \\underline{TE}nsor \\underline{D}ecomposition for binary and count tensors. Specifically, we first employ a nonparametric Gaussian process (GP) to replace traditional multi-linear structures. Next, we utilize the \\pg augmentation which provides a unified framework to establish conjugate models for binary and count distributions. Finally, to address the computational issue of GPs, we enhance the model by incorporating sparse orthogonal variational inference of inducing points, which offers a more effective covariance approximation within GPs and stochastic natural gradient updates for nonparametric models. We evaluate our model on several real-world tensor completion tasks, considering binary and count datasets. The results manifest both better performance and computational advantages of the proposed model.","url_abs":"https://arxiv.org/abs/2401.07711v1","url_pdf":"https://arxiv.org/pdf/2401.07711v1.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":"efficient-nonparametric-tensor-decomposition","repo_url":"https://github.com/taozerui/gptd","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"tensor-decomposition","task_name":"Tensor Decomposition"},{"task_slug":"variational-inference","task_name":"Variational Inference"}],"methods":[{"method_slug":"gps","method_name":"GPS"},{"method_slug":"gaussian-process","method_name":"Gaussian Process"},{"method_slug":"tucker","method_name":"TuckER"},{"method_slug":"variational-inference","method_name":"Variational Inference"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2401.07711","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2401.07711"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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