{"ID":2825118,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.21486","arxiv_id":"2512.21486","title":"When Bayesian Tensor Completion Meets Multioutput Gaussian Processes: Functional Universality and Rank Learning","abstract":"Functional tensor decomposition can analyze multi-dimensional data with real-valued indices, paving the path for applications in machine learning and signal processing. A limitation of existing approaches is the assumption that the tensor rank-a critical parameter governing model complexity-is known. However, determining the optimal rank is a non-deterministic polynomial-time hard (NP-hard) task and there is a limited understanding regarding the expressive power of functional low-rank tensor models for continuous signals. We propose a rank-revealing functional Bayesian tensor completion (RR-FBTC) method. Modeling the latent functions through carefully designed multioutput Gaussian processes, RR-FBTC handles tensors with real-valued indices while enabling automatic tensor rank determination during the inference process. We establish the universal approximation property of the model for continuous multi-dimensional signals, demonstrating its expressive power in a concise format. To learn this model, we employ the variational inference framework and derive an efficient algorithm with closed-form updates. Experiments on both synthetic and real-world datasets demonstrate the effectiveness and superiority of the RR-FBTC over state-of-the-art approaches. The code is available at https://github.com/OceanSTARLab/RR-FBTC.","short_abstract":"Functional tensor decomposition can analyze multi-dimensional data with real-valued indices, paving the path for applications in machine learning and signal processing. A limitation of existing approaches is the assumption that the tensor rank-a critical parameter governing model complexity-is known. However, determini...","url_abs":"https://arxiv.org/abs/2512.21486","url_pdf":"https://arxiv.org/pdf/2512.21486v1","authors":"[\"Siyuan Li\",\"Shikai Fang\",\"Lei Cheng\",\"Feng Yin\",\"Yik-Chung Wu\",\"Peter Gerstoft\",\"Sergios Theodoridis\"]","published":"2025-12-25T03:15:52Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"eess.SP\"]","methods":"[]","has_code":false,"code_links":[{"ID":605638,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_id":2825118,"paper_url":"https://arxiv.org/abs/2512.21486","paper_title":"When Bayesian Tensor Completion Meets Multioutput Gaussian Processes: Functional Universality and Rank Learning","repo_url":"https://github.com/OceanSTARLab/RR-FBTC","is_official":false,"mentioned_in_paper":false,"mentioned_in_github":true,"github_stars":0}]}