Approximate Message Passing algorithms for rotationally invariant matrices
旋转不变矩阵的近似消息传递算法AI 解读 ↓
← 返回论文列表与筛选
阅读说明
本页整理公开书目信息，不生成学术质量评分。AI 解读根据题名及所注明的摘要或原文片段生成，未完成全文核验，可能有误；具体假设、证明与结论请核对原文。摘要保留来源文本，未经模型改写。
DOI 首次登记不等于接收或发表日期。部分更正、评论等条目没有独立摘要；缺少可靠材料时保留待补状态。
引用量采用 OpenAlex 单条关联记录，不合计多个记录；关联记录可能包含正式发表版本，不等于此版本单独引用。缺失不视为零，引用指标不代表论文质量。
关注作者按书目中的完整姓名匹配，同名和姓名变体需人工辨别。相关论文先按共享细分方向和具体方法排列，再参考通用方法与发表日期。
分类依据与纠错
AI 根据所提供的论文材料归类：摘要讨论随机矩阵和一般主成分算法，未明确建立宏观或金融因子模型。
反馈分类问题
正在核对关联版本…
代码、数据与补充材料
正在核对对应版本的资源…
关注这篇论文的作者
旋转不变矩阵的近似消息传递算法
- 研究问题
- 当随机矩阵具有正交旋转不变性但噪声谱不同于白噪声时，如何确定AMP的修正项和状态演化并用于主成分估计？
- 方法与思路
- 作者用谱分布的自由累积量或矩形自由累积量定义Onsager修正与状态演化，并研究具有主成分先验的Bayes-AMP。
- 材料陈述的贡献
- 摘要称严格证明了此前非严格推导的公式，并在足够强信号与非高斯主成分先验下证明估计精度优于样本主成分。
- 阅读关注点
- 应核对旋转不变矩阵的条件、状态演化适用范围、信号强度门槛，以及与样本主成分比较时的损失和先验要求。
- 阅读边界
- 仅据版本未注明的OpenAlex摘要，不能将有条件的精度改进推广到任意矩阵、信号强度或先验，也不能推断刊本变化。
原文摘要
Approximate Message Passing (AMP) algorithms have seen widespread use across a variety of applications. However, the precise forms for their Onsager corrections and state evolutions depend on properties of the underlying random matrix ensemble, limiting the extent to which AMP algorithms derived for white noise may be applicable to data matrices that arise in practice. In this work, we study more general AMP algorithms for random matrices W that satisfy orthogonal rotational invariance in law, where W may have a spectral distribution that is different from the semicircle and Marcenko–Pastur laws characteristic of white noise. The Onsager corrections and state evolutions in these algorithms are defined by the free cumulants or rectangular free cumulants of the spectral distribution of W. Their forms were derived previously by Opper, Çakmak and Winther using nonrigorous dynamic functional theory techniques, and we provide rigorous proofs. Our motivating application is a Bayes-AMP algorithm for Principal Components Analysis, when there is prior structure for the principal components (PCs) and possibly nonwhite noise. For sufficiently large signal strengths and any non-Gaussian prior distributions for the PCs, we show that this algorithm provably achieves higher estimation accuracy than the sample PCs.