12 research outputs found
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
Robust phase retrieval with the swept approximate message passing (prSAMP) algorithm
In phase retrieval, the goal is to recover a complex signal from the
magnitude of its linear measurements. While many well-known algorithms
guarantee deterministic recovery of the unknown signal using i.i.d. random
measurement matrices, they suffer serious convergence issues some
ill-conditioned matrices. As an example, this happens in optical imagers using
binary intensity-only spatial light modulators to shape the input wavefront.
The problem of ill-conditioned measurement matrices has also been a topic of
interest for compressed sensing researchers during the past decade. In this
paper, using recent advances in generic compressed sensing, we propose a new
phase retrieval algorithm that well-adopts for both Gaussian i.i.d. and binary
matrices using both sparse and dense input signals. This algorithm is also
robust to the strong noise levels found in some imaging applications
VON MISES PRIOR FOR PHASE-NOISY DOA ESTIMATION: THE VITAMIN ALGORITHM
International audienceSound waves in the ocean are affected by the space and time variabilities of the propagation medium. These fluctuations, mainly caused by internal waves such as tides and gyres, can lead to a loss of phase information in measured wave-fronts, and make hardly predictable the true location of a source. As a consequence, the performance of classical direction of arrival (DOA) estimation algorithms are significantly degraded. An important literature addresses this issue by considering either the phase as non-informative or the environment as a noise with no physical information. In this work, we propose to introduce a phase prior inspired by random fluctuation theories. This prior is combined with a sparsity assumption on the number of expected DOAs and exploited within a Bayesian framework. The contributions of such an approach are twofold: by the use of suitable prior information (small number of DOAs and phase distortion), it allows an estimation of DOAs from a single snapshot , while simultaneously providing a posterior estimation of the mean fluctuations of the propagation medium. Bayesian inference can be performed in different ways. Among the different possible procedures, we chose here to resort to a Bethe approximation and a message-passing approach recently considered in compressive sensing setups. The resulting algorithm places in the continuation of our previous works. The main improvement lies in the proba-bilistic model used to describe the phase distortion. Here we use a Multivariate Von Mises distribution, more suitable to directional statistics and still fitting the simplified theory of phase fluctuation. Numerical experiments with synthetic datasets show that the proposed algorithm , dubbed as VITAMIN for ``Von mIses swepT Approximate Message passINg'', presents interesting performance compared to other state-of-the-art algorithms. In particular, in the considered experiments, VITAMIN behaves well regarding its robustness to additive noise and phase fluctuations
Hybrid approximate message passing
Gaussian and quadratic approximations of message passing algorithms on graphs have attracted considerable recent attention due to their computational simplicity, analytic tractability, and wide applicability in optimization and statistical inference problems. This paper presents a systematic framework for incorporating such approximate message passing (AMP) methods in general graphical models. The key concept is a partition of dependencies of a general graphical model into strong and weak edges, with the weak edges representing interactions through aggregates of small, linearizable couplings of variables. AMP approximations based on the Central Limit Theorem can be readily applied to aggregates of many weak edges and integrated with standard message passing updates on the strong edges. The resulting algorithm, which we call hybrid generalized approximate message passing (HyGAMP), can yield significantly simpler implementations of sum-product and max-sum loopy belief propagation. By varying the partition of strong and weak edges, a performance--complexity trade-off can be achieved. Group sparsity and multinomial logistic regression problems are studied as examples of the proposed methodology.The work of S. Rangan was supported in part by the National Science Foundation under Grants 1116589, 1302336, and 1547332, and in part by the industrial affiliates of NYU WIRELESS. The work of A. K. Fletcher was supported in part by the National Science Foundation under Grants 1254204 and 1738286 and in part by the Office of Naval Research under Grant N00014-15-1-2677. The work of V. K. Goyal was supported in part by the National Science Foundation under Grant 1422034. The work of E. Byrne and P. Schniter was supported in part by the National Science Foundation under Grant CCF-1527162. (1116589 - National Science Foundation; 1302336 - National Science Foundation; 1547332 - National Science Foundation; 1254204 - National Science Foundation; 1738286 - National Science Foundation; 1422034 - National Science Foundation; CCF-1527162 - National Science Foundation; NYU WIRELESS; N00014-15-1-2677 - Office of Naval Research