Hybrid Approximate Message Passing

Sundeep Rangan, Alyson K. Fletcher, Vivek K. Goyal, Evan Byrne, Philip Schniter

Research output: Contribution to journalArticlepeer-review


Gaussian and quadratic approximations of message passing algorithms on graphs have attracted considerable recent attention due to their computational simplicity, analytic tractability, and wide applicability in optimization and statistical inference problems. This paper presents a systematic framework for incorporating such approximate message passing (AMP) methods in general graphical models. The key concept is a partition of dependencies of a general graphical model into strong and weak edges, with the weak edges representing small, linearizable couplings of variables. AMP approximations based on the central limit theorem can be readily applied to aggregates of many weak edges and integrated with standard message passing updates on the strong edges. The resulting algorithm, which we call hybrid generalized approximate message passing (HyGAMP), can yield significantly simpler implementations of sum-product and max-sum loopy belief propagation. By varying the partition of strong and weak edges, a performance-complexity tradeoff can be achieved. Group sparsity and multinomial logistic regression problems are studied as examples of the proposed methodology.

Original languageEnglish (US)
Article number7944630
Pages (from-to)4577-4592
Number of pages16
JournalIEEE Transactions on Signal Processing
Issue number17
StatePublished - Sep 1 2017


  • Approximate message passing
  • belief propagation
  • group sparsity
  • max-sum algorithm
  • multinomial logistic regression
  • sum-product algorithm

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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