Tensor Generalized Approximate Message Passing
This provides a more efficient method for researchers and practitioners working with tensor data in machine learning and signal processing, though it appears incremental as an extension of existing AMP methods to tensors.
The authors tackled low-rank tensor inference problems like tensor completion and decomposition by proposing a tensor generalized approximate message passing (TeG-AMP) algorithm, which significantly improves recovery performance by leveraging tensor structures.
We propose a tensor generalized approximate message passing (TeG-AMP) algorithm for low-rank tensor inference, which can be used to solve tensor completion and decomposition problems. We derive TeG-AMP algorithm as an approximation of the sum-product belief propagation algorithm in high dimensions where the central limit theorem and Taylor series approximations are applicable. As TeG-AMP is developed based on a general TR decomposition model, it can be directly applied to many low-rank tensor types. Moreover, our TeG-AMP can be simplified based on the CP decomposition model and a tensor simplified AMP is proposed for low CP-rank tensor inference problems. Experimental results demonstrate that the proposed methods significantly improve recovery performances since it takes full advantage of tensor structures.