As we all know AMP solvers are a big deal because very few iterations are needed and because every iteration involve low complexity matrix-vecotr multiplies. So yesterday, after I featured Inference for Generalized Linear Models via Alternating Directions and Bethe Free Energy Minimization one of the authors, Phil Schniter, followed through with:
Thanks for helping to publicize our work on ADMM-GAMP. I wanted to clarify something, though. Rather than being merely an "alternative to SwAMP," it is the first (to our knowledge) AMP-based algorithm that is provably convergent for arbitrary linear transforms. As you know, AMP is not well trusted because it does not always converge, and this defect has spawned various heuristic fixes such as damping (http://arxiv.org/abs/1402.321
0), adaptive damping (http://arxiv.org/abs/1412.200 5), and serial updating (i.e., SWAMP). Although they seem to work well in practice, they still lack convergence guarantees. And so we are pretty excited about ADMM-GAMP, especially in the context of MMSE estimation (since MAP estimation is already well served by many existing convex solvers).
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