When Bayesian Tensor Completion Meets Multioutput Gaussian Processes: Functional Universality and Rank Learning

2025/12/25 by Siyuan Li, Li, Siyuan, Shikai Fang +11
Computer Science · Engineering · Mathematics · #FOS: Computer and information sciences #FOS: Electrical engineering #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Signal Processing (eess.SP) #Sparse and Compressive Sensing Techniques #Tensor decomposition and applications #electronic engineering #information engineering

paper · doi:10.48550/arxiv.2512.21486

openalex publication_date 2025/12/25 · openalex created_date 2025/12/30 · openalex updated_date 2026/07/28

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.

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Related

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• Robust Factorization and Completion of Streaming Tensor Data via Variational Bayesian Inference