Large-Scale Bayesian Tensor Reconstruction: An Approximate Message Passing Solution
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914275993321472 |
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| author | Cheng, Bingyang Chen, Zhongtao Jin, Yichen Zhang, Hao Zhang, Chen Lam, Edmund Y. Wu, Yik-Chung |
| author_facet | Cheng, Bingyang Chen, Zhongtao Jin, Yichen Zhang, Hao Zhang, Chen Lam, Edmund Y. Wu, Yik-Chung |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_16305 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Large-Scale Bayesian Tensor Reconstruction: An Approximate Message Passing Solution Cheng, Bingyang Chen, Zhongtao Jin, Yichen Zhang, Hao Zhang, Chen Lam, Edmund Y. Wu, Yik-Chung Machine Learning Signal Processing 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. |
| title | Large-Scale Bayesian Tensor Reconstruction: An Approximate Message Passing Solution |
| topic | Machine Learning Signal Processing |
| url | https://arxiv.org/abs/2505.16305 |