Unifying AMP Algorithms for Rotationally-Invariant Models
This work provides a theoretical unification for AMP algorithms, which is incremental but clarifies foundational aspects like free cumulants in signal processing and statistical estimation.
The paper tackles the problem of constructing Approximate Message Passing (AMP) algorithms for rotationally-invariant models by presenting a unified framework that systematically derives correct Onsager terms, rederives an existing AMP algorithm, and introduces two novel AMP variants applied to spiked models.
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.