统一构建旋转不变模型的近似消息传递算法，提升精度与适用性。
Unifying AMP Algorithms for Rotationally-Invariant Models
- 基于通用迭代模板推导出带正确补偿项的正交AMP算法。
- 重新推导已有算法，并揭示谱分布自由累积量的内在作用。
- 提出两种新变体，适用于稀疏信号估计等场景。
本文提出一个统一框架，用于构建旋转不变模型的近似消息传递（AMP）算法。通过采用通用迭代算法模板并简化为长记忆正交AMP（OAMP），系统推导出AMP算法中正确的Onsager修正项。该方法使我们重新推导出Fan与Opper等人提出的AMP算法，并揭示了谱律自由累积量在其中的作用。自由累积量源于递归中心化操作，可能具有独立研究价值。为展示框架灵活性，我们引入两种新型AMP变体，并将其应用于脉冲模型中的估计问题。
原文摘要 · Abstract (English)
This paper presents a unified framework for constructing Approximate Message Passing (AMP) algorithms for rotationally-invariant models. By employing a general iterative algorithm template and reducing it to long-memory Orthogonal AMP (OAMP), we systematically derive the correct Onsager terms of AMP algorithms. This approach allows us to rederive an AMP algorithm introduced by Fan and Opper et al., while shedding new light on the role of free cumulants of the spectral law. The free cumulants arise naturally from a recursive centering operation, potentially of independent interest beyond the scope of AMP. To illustrate the flexibility of our framework, we introduce two novel AMP variants and apply them to estimation in spiked models.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。