mlsanityData to 7 Oct 2026

Unifying AMP Algorithms for Rotationally-Invariant Models

arXiv 2412.01574 ↗First posted 2 Dec 2024math.ST cs.IT cs.LGcited by 3

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Abstract (arXiv)

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.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 20 of its 65 references that are in the map. First posted on arXiv 2 Dec 2024.

Builds on

20 of 65 references.

References · 20

  1. 2013Expectation Propagation for approximate Bayesian inferencecited by 172
  2. 2017Optimal Errors and Phase Transitions in High-Dimensional Generalized Linear Modelscited by 115
  3. 2018A modern maximum-likelihood theory for high-dimensional logistic regressioncited by 79
  4. 2021A unifying tutorial on Approximate Message Passingcited by 49
  5. 2017Estimation of Low-Rank Matrices via Approximate Message Passingcited by 41
  6. 2020The estimation error of general first order methodscited by 33
  7. 2020Approximate Message Passing algorithms for rotationally invariant matricescited by 31
  8. 2014Phase transitions and sample complexity in Bayes-optimal matrix factorizationcited by 22
  9. 2021Approximate Message Passing for orthogonally invariant ensembles: Multivariate non-linearities and spectral initializationcited by 18
  10. 2021Estimation in Rotationally Invariant Generalized Linear Models via Approximate Message Passingcited by 18
  11. 2022A Non-Asymptotic Framework for Approximate Message Passing in Spiked Modelscited by 18
  12. 2019Inference with Deep Generative Priors in High Dimensionscited by 17
8 more
  1. 2019Algorithmic Analysis and Statistical Estimation of SLOPE via Approximate Message Passingcited by 14
  2. 2017Inference in Deep Networks in High Dimensionscited by 12
  3. 2020Optimization of Mean-field Spin Glassescited by 9
  4. 2020Memory AMPcited by 9
  5. 2023Approximate message passing from random initialization with applications to mathbbZ2 synchronizationcited by 9
  6. 2024Information limits and Thouless-Anderson-Palmer equations for spiked matrix models with structured noisecited by 6
  7. 2022Approximate Message Passing for Multi-Layer Estimation in Rotationally Invariant Modelscited by 3
  8. 2024Optimality of Approximate Message Passing Algorithms for Spiked Matrix Models with Rotationally Invariant Noisecited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 1; 2025: 1; 2026: 1.

3 papers.

  1. 2025The Effect of Optimal Self-Distillation in Noisy Gaussian Mixture Modelcited by 1
  2. 2024Robust Random Graph Matching in Dense Graphs via an Approximate Message Passing Type Algorithmcited by 0
  3. 2026Decoupled Descent: Exact Test Error Tracking Via Approximate Message Passingcited by 0