Large-Scale Bayesian Tensor Reconstruction: An Approximate Message Passing Solution
This work addresses scalability issues in Bayesian tensor decomposition for applications like data analysis, though it is incremental as it builds on existing GAMP methods.
The paper tackles the problem of scaling Bayesian tensor reconstruction for large tensors by introducing CP-GAMP, which reduces runtime by 82.7% compared to state-of-the-art methods while maintaining accuracy on synthetic data with 20% observed elements.
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.