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Approximate Message Passing for sparse matrices with application to the equilibria of large ecological Lotka–Volterra systems

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  • Hachem, Walid

Abstract

This paper is divided into two parts. The first part is devoted to the study of a class of Approximate Message Passing (AMP) algorithms which are widely used in the fields of statistical physics, machine learning, or communication theory. The AMP algorithms studied in this part are those where the measurement matrix has independent elements, up to the symmetry constraint when this matrix is symmetric, with a variance profile that can be sparse. The AMP problem is solved by adapting the approach of Bayati, Lelarge, and Montanari (2015) to this matrix model.

Suggested Citation

  • Hachem, Walid, 2024. "Approximate Message Passing for sparse matrices with application to the equilibria of large ecological Lotka–Volterra systems," Stochastic Processes and their Applications, Elsevier, vol. 170(C).
    • Handle: RePEc:eee:spapps:v:170:y:2024:i:c:s030441492300248x
    DOI: 10.1016/j.spa.2023.104276
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