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Vector Approximate Message Passing for the Generalized Linear Model
The generalized linear model (GLM), where a random vector is
observed through a noisy, possibly nonlinear, function of a linear transform
output , 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 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 , 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 to the larger class of rotationally invariant
. 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 than damped GAMP
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