19 research outputs found
Fixed Points of Generalized Approximate Message Passing with Arbitrary Matrices
The estimation of a random vector with independent components passed through a linear transform followed by a componentwise (possibly nonlinear) output map arises in a range of applications. Approximate message passing (AMP) methods, based on Gaussian approximations of loopy belief propagation, have recently attracted considerable attention for such problems. For large random transforms, these methods exhibit fast convergence and admit precise analytic characterizations with testable conditions for optimality, even for certain non-convex problem instances. However, the behavior of AMP under general transforms is not fully understood. In this paper, we consider the generalized AMP (GAMP) algorithm and relate the method to more common optimization techniques. This analysis enables a precise characterization of the GAMP algorithm fixed-points that applies to arbitrary transforms. In particular, we show that the fixed points of the so-called max-sum GAMP algorithm for MAP estimation are critical points of a constrained maximization of the posterior density. The fixed-points of the sum-product GAMP algorithm for estimation of the posterior marginals can be interpreted as critical points of a certain mean-field variational optimization. Index Terms—Belief propagation, ADMM, variational optimization, message passing
Precoding via Approximate Message Passing with Instantaneous Signal Constraints
This paper proposes a low complexity precoding algorithm based on the
recently proposed Generalized Least Square Error (GLSE) scheme with generic
penalty and support. The algorithm iteratively constructs the transmit vector
via Approximate Message Passing (AMP). Using the asymptotic decoupling property
of GLSE precoders, we derive closed form fixed point equations to tune the
parameters in the proposed algorithm for a general set of instantaneous signal
constraints. The tuning strategy is then utilized to construct transmit vectors
with restricted peak-to-average power ratios and to efficiently select a subset
of transmit antennas. The numerical investigations show that the proposed
algorithm tracks the large-system performance of GLSE precoders even for a
moderate number of antennas.Comment: 2018 International Zurich Seminar on Information and Communication
(IZS) 5 pages and 2 figure
Binary Linear Classification and Feature Selection via Generalized Approximate Message Passing
For the problem of binary linear classification and feature selection, we
propose algorithmic approaches to classifier design based on the generalized
approximate message passing (GAMP) algorithm, recently proposed in the context
of compressive sensing. We are particularly motivated by problems where the
number of features greatly exceeds the number of training examples, but where
only a few features suffice for accurate classification. We show that
sum-product GAMP can be used to (approximately) minimize the classification
error rate and max-sum GAMP can be used to minimize a wide variety of
regularized loss functions. Furthermore, we describe an
expectation-maximization (EM)-based scheme to learn the associated model
parameters online, as an alternative to cross-validation, and we show that
GAMP's state-evolution framework can be used to accurately predict the
misclassification rate. Finally, we present a detailed numerical study to
confirm the accuracy, speed, and flexibility afforded by our GAMP-based
approaches to binary linear classification and feature selection