提出新算法提升低秩张量恢复效果，可处理多种张量类型。
Tensor Generalized Approximate Message Passing
- 基于张量分解模型设计近似消息传递算法，利用中心极限定理简化计算。
- 在张量补全与分解任务中表现优于传统方法，显著提升恢复精度。
- 适用于低CP秩张量问题，适合需要高效结构化推理的研究者。
我们提出一种张量广义近似消息传递（TeG-AMP）算法，用于低秩张量推断，可解决张量补全与分解问题。该算法是高维场景下和积信念传播的近似，依赖中心极限定理与泰勒展开。由于基于通用TR分解模型，可直接应用于多种低秩张量。此外，针对CP分解模型可进一步简化，提出张量简化AMP算法，适用于低CP秩张量推断。实验表明，所提方法充分利用张量结构，在恢复性能上显著优于现有方法。
原文摘要 · Abstract (English)
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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