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arXiv · 2504.00008

Tensor Generalized Approximate Message Passing

Yinchuan Li·Guangchen Lan·Xiaodong Wang
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Abstract

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.

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Yinchuan Li, Guangchen Lan, Xiaodong Wang. 2025-03-25. Tensor Generalized Approximate Message Passing. https://arxiv.org/abs/2504.00008

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