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Communication Dans Un Congrès Année : 2023

Towards Convergent Approximate Message Passing by Alternating Constrained Minimization of Bethe Free Energy

Résumé

Generalized Approximate Message Passing (GAMP) allows for Bayesian inference in linear models with non-identically independently distributed (n.i.i.d.) priors and n.i.i.d. measurements of the linear mixture outputs. It represents an efficient technique for approximate inference, which becomes accurate when both rows and columns of the measurement matrix can be treated as sets of independent vectors and both dimensions become large. It has been shown that the fixed points of GAMP correspond to the extrema of a large system limit of the Bethe Free Energy (LSL-BFE), which represents a meaningful approximation optimization criterion regardless of whether the measurement matrix exhibits the independence properties. However, the convergence of (G)AMP can be problematic for certain measurement matrices. In this paper, we revisit the GAMP algorithm by applying a simplified version of the Alternating Direction Method of Multipliers (ADMM) to minimizing the LSLBFE. We show convergence of the mean and variance subsystems in AMBGAMP and in the Gaussian case, convergence of mean and LSL variance to the Minimum Mean Squared Error (MMSE) quantities.
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Dates et versions

hal-04189307 , version 1 (28-08-2023)

Identifiants

Citer

Christo Kurisummoottil Thomas, Zilu Zhao, Dirk Slock. Towards Convergent Approximate Message Passing by Alternating Constrained Minimization of Bethe Free Energy. 2023 IEEE Information Theory Workshop (ITW), Apr 2023, Saint-Malo, France. pp.299-304, ⟨10.1109/ITW55543.2023.10161629⟩. ⟨hal-04189307⟩

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