With only one week left to register for iTWIST’16, I am going to walk you through the rest of our keynote speakers this week.
Our next speaker is Phil Schniter. Phil Schniter is Professsor in Electrical and Computer Engineering at Department of Electrical and Computer Engineering at Ohio State University, USA.
Professor Schniter joined the Department of Electrical and Computer Engineering at OSU after graduating with a PhD in Electrical Engineering from Cornell University in 2000. Phil Schniter also has industrial experience from Tektronix from 1993 to 1996 and has been a visiting professor at Eurecom (Sophia Antipolis, France) from October 2008 through February 2009, and at Supelec (Gif sur Yvette, France) from March 2009 through August 2009.
Professor Schniter has published an impressive selection of research papers; previously especially within digital communication. In recent years he has been very active in the research around generalised approximate message passing (GAMP). GAMP is an estimation framework that has become popular in compressed sensing / sparse estimation. The reasons for the success of this algorithm (family), as I see it, are that the algorithm estimates under-sampled sparse vectors with comparable accuracy to the classic l1-minimisation approach in compressed sensing and favourable computational complexity. At the same time, the framework is easily adaptable to many kinds of different signal distributions and other types of structure than plain sparsity. If you are dealing with a signal that is not distributed according to the Laplace distribution that the l1-minimisation approach implies, you can adapt GAMP to this other (known) distribution and achieve better reconstruction capabilities than the l1-minimisation. Even if you don’t know the distribution, GAMP can also be modified to estimate it automatically and quite efficiently. This and many other details are among Professor Schniter’s contributions to the research on GAMP.
At this year’s iTWIST, Phil Schniter will be describing recent work on robust variants of GAMP. In details, the abstract reads (and this is joint work with Alyson Fletcher and Sundeep Rangan):
Robust approximate message passing
Approximate message passing (AMP) has recently become popular for inference in linear and generalized linear models. AMP can be viewed as an approximation of loopy belief propagation that requires only two matrix multiplies and a (typically simple) denoising step per iteration, and relatively few iterations, making it computationally efficient. When the measurement matrix “A” is large and well modeled as i.i.d. sub-Gaussian, AMP’s behavior is closely predicted by a state evolution. Furthermore, when this state evolution has unique fixed points, the AMP estimates are Bayes optimal. For general measurement matrices, however, AMP may produce highly suboptimal estimates or not even converge. Thus, there has been great interest in making AMP robust to the choice of measurement matrix.
In this talk, we describe some recent progress on robust AMP. In particular, we describe a method based on an approximation of non-loopy expectation propagation that, like AMP, requires only two matrix multiplies and a simple denoising step per iteration. But unlike AMP, it leverages knowledge of the measurement matrix SVD to yield excellent performance over a larger class of measurement matrices. In particular, when the Gramian A’A is large and unitarily invariant, its behavior is closely predicted by a state evolution whose fixed points match the replica prediction. Moreover, convergence has been proven in certain cases, with empirical results showing robust convergence even with severely ill-conditioned matrices. Like AMP, this robust AMP can be successfully used with non-scalar denoisers to accomplish sophisticated inference tasks, such as simultaneously learning and exploiting i.i.d. signal priors, or leveraging black-box denoisers such as BM3D. We look forward to describing these preliminary results, as well as ongoing research, on robust AMP.