When Bayesian Tensor Completion Meets Multioutput Gaussian Processes: Functional Universality and Rank Learning
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arXiv
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| Autori principali: | , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912789095776256 |
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| author | Li, Siyuan Fang, Shikai Cheng, Lei Yin, Feng Wu, Yik-Chung Gerstoft, Peter Theodoridis, Sergios |
| author_facet | Li, Siyuan Fang, Shikai Cheng, Lei Yin, Feng Wu, Yik-Chung Gerstoft, Peter Theodoridis, Sergios |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21486 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | When Bayesian Tensor Completion Meets Multioutput Gaussian Processes: Functional Universality and Rank Learning Li, Siyuan Fang, Shikai Cheng, Lei Yin, Feng Wu, Yik-Chung Gerstoft, Peter Theodoridis, Sergios Machine Learning Signal Processing 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. |
| title | When Bayesian Tensor Completion Meets Multioutput Gaussian Processes: Functional Universality and Rank Learning |
| topic | Machine Learning Signal Processing |
| url | https://arxiv.org/abs/2512.21486 |