On convergence of approximate message passing

Francesco Caltagirone (1) , Florent Krzakala (2, 3) , Lenka Zdeborová (1)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681
2 Gulliver (UMR 7083)
3 ESPCI Paris - Ecole Superieure de Physique et de Chimie Industrielles de la Ville de Paris

Approximate message passing is an iterative algorithm for compressed sensing and related applications. A solid theory about the performance and convergence of the algorithm exists for measurement matrices having iid entries of zero mean. However, it was observed by several authors that for more general matrices the algorithm often encounters convergence problems. In this paper we identify the reason of the non-convergence for measurement matrices with iid entries and non-zero mean in the context of Bayes optimal inference. Finally we demonstrate numerically that when the iterative update is changed from parallel to sequential the convergence is restored.

Domaines: Physique [physics]

Francesco Caltagirone, Florent Krzakala, Lenka Zdeborová. On convergence of approximate message passing. ISIT 2014 - 2014 IEEE International Symposium on Information Theory, IEEE, Jun 2014, Honolulu, United States. pp.1812-1816, ⟨10.1109/ISIT.2014.6875146⟩. ⟨cea-01223403⟩