Paper Info
Title
Vector Approximate Message Passing For The Generalized Linear Model
Abstract
The generalized linear model (GLM), where a random vector x is observed through a noisy, possibly nonlinear, function of a linear transform output z = Ax, arises in a range of applications such as robust regression, binary classification, quantized compressed sensing, phase retrieval, photon-limited imaging, and inference from neural spike trains. When A is large and i.i.d. Gaussian, the generalized approximate message passing (GAMP) algorithm is an efficient means of MAP or marginal inference, and its performance can be rigorously characterized by a scalar state evolution. For general A, though, GAMP can misbehave. Damping and sequential-updating help to robustify GAMP, but their effects are limited. Recently, a "vector AMP" (VAMP) algorithm was proposed for additive white Gaussian noise channels. VAMP extends AMP's guarantees from i.i.d. Gaussian A to the larger class of rotationally invariant A. In this paper, we show how VAMP can be extended to the GLM. Numerical experiments show that the proposed GLM-VAMP is much more robust to ill-conditioning in A than damped GAMP.
Year
DOI
Venue
2016
10.1109/ACSSC.2016.7869633
2016 50TH ASILOMAR CONFERENCE ON SIGNALS, SYSTEMS AND COMPUTERS
DocType
Volume
ISSN
Conference
abs/1612.01186
1058-6393
Citations 
PageRank 
References 
0
0.34
0
Authors
3
Name
Order
Citations
PageRank
Philip Schniter1162093.74
Sundeep Rangan23101163.90
Alyson K. Fletcher355241.10