Large-Scale Bayesian Tensor Reconstruction: An Approximate Message Passing Solution
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.
Cite
@article{arxiv.2505.16305,
title = {Large-Scale Bayesian Tensor Reconstruction: An Approximate Message Passing Solution},
author = {Bingyang Cheng and Zhongtao Chen and Yichen Jin and Hao Zhang and Chen Zhang and Edmund Y. Lam and Yik-Chung Wu},
journal= {arXiv preprint arXiv:2505.16305},
year = {2026}
}