正交近似信息传递算法用于具有旋转不变噪声的矩形尖峰矩阵模型
Orthogonal Approximate Message Passing Algorithms for Rectangular Spiked Matrix Models with Rotationally Invariant Noise
AI总结：
本文提出了一种正交近似信息传递算法，用于在具有旋转不变噪声的矩形尖峰矩阵模型中进行信号估计，并证明其在特定噪声条件下具有最优性能。
摘要：
我们提出了一种正交近似信息传递（OAMP）算法，用于在具有通用旋转不变（RI）噪声的矩形尖峰矩阵模型中进行信号估计。我们建立了严格的态演化，精确刻画了该算法的高维动态。在此框架基础上，我们推导出一种最优的OAMP变种，该变种在每次迭代中最小化预测的均方误差。对于独立同分布高斯噪声的特殊情况，所提出的OAMP算法的固定点与标准AMP算法的固定点一致。对于一般的RI噪声模型，我们推测最优的OAMP算法在广泛的迭代方法类中是统计最优的，并在某些情况下实现贝叶斯最优性能。
英文摘要：
We propose an orthogonal approximate message passing (OAMP) algorithm for signal estimation in the rectangular spiked matrix model with general rotationally invariant (RI) noise. We establish a rigorous state evolution that exactly characterizes the high-dimensional dynamics of the algorithm. Building on this framework, we derive an optimal variant of OAMP that minimizes the predicted mean-squared error at each iteration. For the special case of i.i.d. Gaussian noise, the fixed point of the proposed OAMP algorithm coincides with that of the standard AMP algorithm. For general RI noise models, we conjecture that the optimal OAMP algorithm is statistically optimal within a broad class of iterative methods, and achieves Bayes-optimal performance in certain regimes.
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