mlsanityData to 7 Oct 2026

Multi-Layer Generalized Linear Estimation

arXiv 1701.06981 ↗First posted 24 Jan 2017cs.IT cond-mat.stat-mech math.ITcited by 12

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Abstract (arXiv)

We consider the problem of reconstructing a signal from multi-layered (possibly) non-linear measurements. Using non-rigorous but standard methods from statistical physics we present the Multi-Layer Approximate Message Passing (ML-AMP) algorithm for computing marginal probabilities of the corresponding estimation problem and derive the associated state evolution equations to analyze its performance. We also give the expression of the asymptotic free energy and the minimal information-theoretically achievable reconstruction error. Finally, we present some applications of this measurement model for compressed sensing and perceptron learning with structured matrices/patterns, and for a simple model of estimation of latent variables in an auto-encoder.

Key facts. Cited by 12 papers in the map (data through 7 Oct 2026). First posted on arXiv 24 Jan 2017.

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Citing papers per year: 2021: 5; 2022: 1; 2023: 3; 2024: 3.

12 papers.

  1. 2021Learning Gaussian Mixtures with Generalised Linear Models: Precise Asymptotics in High-dimensionscited by 52
  2. 2021Graph-based Approximate Message Passing Iterationscited by 35
  3. 2023Deterministic equivalent and error universality of deep random features learningcited by 35
  4. 2024Asymptotics of Learning with Deep Structured (Random) Featurescited by 13
  5. 2021Deep learning via message passing algorithms based on belief propagationcited by 12
  6. 2024High-dimensional learning of narrow neural networkscited by 12
  7. 2024Information limits and Thouless-Anderson-Palmer equations for spiked matrix models with structured noisecited by 6
  8. 2021Memory Approximate Message Passingcited by 4
  9. 2023Neural-prior stochastic block modelcited by 4
  10. 2022Approximate Message Passing for Multi-Layer Estimation in Rotationally Invariant Modelscited by 3
  11. 2021Sufficient-Statistic Memory AMPcited by 2
  12. 2023Bayes optimal learning in high-dimensional linear regression with network side informationcited by 2