Large-Scale Bayesian Tensor Reconstruction: An Approximate Message Passing Solution

• URL: http://arxiv.org/abs/2505.16305v1
• Date: Thu, 22 May 2025 06:57:49 GMT
• Title: Large-Scale Bayesian Tensor Reconstruction: An Approximate Message Passing Solution
• Authors: Bingyang Cheng, Zhongtao Chen, Yichen Jin, Hao Zhang, Chen Zhang, Edmud Y. Lam, Yik-Chung Wu,
• Abstract summary: We introduce CP-GAMP, a scalable Bayesian CPD algorithm for large tensors.<n>The proposed algorithm reduces runtime by 82.7% compared to the state-of-the-art variational Bayesian CPD method.
• Score: 18.444283092747977
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Tensor CANDECOMP/PARAFAC decomposition (CPD) is a fundamental model for tensor reconstruction. Although the Bayesian framework allows for principled uncertainty quantification and automatic hyperparameter learning, existing methods do not scale well for large tensors because of high-dimensional matrix inversions. To this end, we introduce CP-GAMP, a scalable Bayesian CPD algorithm. This algorithm leverages generalized approximate message passing (GAMP) to avoid matrix inversions and incorporates an expectation-maximization routine to jointly infer the tensor rank and noise power. Through multiple experiments, for synthetic 100x100x100 rank 20 tensors with only 20% elements observed, the proposed algorithm reduces runtime by 82.7% compared to the state-of-the-art variational Bayesian CPD method, while maintaining comparable reconstruction accuracy.

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