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Register a new userAdaptive Damping and Mean Removal for the Generalized Approximate Message Passing Algorithm
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Philip Schniter
Publication date
2014
fields
Informatics Engineering
and research's language is
English
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The generalized approximate message passing (GAMP) algorithm is an efficient method of MAP or approximate-MMSE estimation of $x$ observed from a noisy version of the transform coefficients $z = Ax$. In fact, for large zero-mean i.i.d sub-Gaussian $A$, GAMP is characterized by a state evolution whose fixed points, when unique, are optimal. For generic $A$, however, GAMP may diverge. In this paper, we propose adaptive damping and mean-removal strategies that aim to prevent divergence. Numerical results demonstrate significantly enhanced robustness to non-zero-mean, rank-deficient, column-correlated, and ill-conditioned $A$.
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In this paper, we extend the bilinear generalized approximate message passing (BiG-AMP) approach, originally proposed for high-dimensional generalized bilinear regression, to the multi-layer case for the handling of cascaded problem such as matrix-factorization problem arising in relay communication among others. Assuming statistically independent matrix entries with known priors, the new algorithm called ML-BiGAMP could approximate the general sum-product loopy belief propagation (LBP) in the high-dimensional limit enjoying a substantial reduction in computational complexity. We demonstrate that, in large system limit, the asymptotic MSE performance of ML-BiGAMP could be fully characterized via a set of simple one-dimensional equations termed state evolution (SE). We establish that the asymptotic MSE predicted by ML-BiGAMP SE matches perfectly the exact MMSE predicted by the replica method, which is well known to be Bayes-optimal but infeasible in practice. This consistency indicates that the ML-BiGAMP may still retain the same Bayes-optimal performance as the MMSE estimator in high-dimensional applications, although ML-BiGAMPs computational burden is far lower. As an illustrative example of the general ML-BiGAMP, we provide a detector design that could estimate the channel fading and the data symbols jointly with high precision for the two-hop amplify-and-forward relay communication systems.
We present a message passing algorithm for localization and tracking in multipath-prone environments that implicitly considers obstructed line-of-sight situations. The proposed adaptive probabilistic data association algorithm infers the position of a mobile agent using multiple anchors by utilizing delay and amplitude of the multipath components (MPCs) as well as their respective uncertainties. By employing a nonuniform clutter model, we enable the algorithm to facilitate the position information contained in the MPCs to support the estimation of the agent position without exact knowledge about the environment geometry. Our algorithm adapts in an online manner to both, the time-varying signal-to-noise-ratio and line-of-sight (LOS) existence probability of each anchor. In a numerical analysis we show that the algorithm is able to operate reliably in environments characterized by strong multipath propagation, even if a temporary obstruction of all anchors occurs simultaneously.
In sketched clustering, a dataset of $T$ samples is first sketched down to a vector of modest size, from which the centroids are subsequently extracted. Advantages include i) reduced storage complexity and ii) centroid extraction complexity independent of $T$. For the sketching methodology recently proposed by Keriven, et al., which can be interpreted as a random sampling of the empirical characteristic function, we propose a sketched clustering algorithm based on approximate message passing. Numerical experiments suggest that our approach is more efficient than the state-of-the-art sketched clustering algorithm CL-OMPR (in both computational and sample complexity) and more efficient than k-means++ when $T$ is large.
This paper considers the massive connectivity problem in an asynchronous grant-free random access system, where a huge number of devices sporadically transmit data to a base station (BS) with imperfect synchronization. The goal is to design algorithms for joint user activity detection, delay detection, and channel estimation. By exploiting the sparsity on both user activity and delays, we formulate a hierarchical sparse signal recovery problem in both the single-antenna and the multiple-antenna scenarios. While traditional compressed sensing algorithms can be applied to these problems, they suffer high computational complexity and often require the perfect statistical information of channel and devices. This paper solves these problems by designing the Learned Approximate Message Passing (LAMP) network, which belongs to model-driven deep learning approaches and ensures efficient performance without tremendous training data. Particularly, in the multiple-antenna scenario, we design three different LAMP structures, namely, distributed, centralized and hybrid ones, to balance the performance and complexity. Simulation results demonstrate that the proposed LAMP networks can significantly outperform the conventional AMP method thanks to their ability of parameter learning. It is also shown that LAMP has robust performance to the maximal delay spread of the asynchronous users.
The generalized approximate message passing (GAMP) algorithm under the Bayesian setting shows advantage in recovering under-sampled sparse signals from corrupted observations. Compared to conventional convex optimization methods, it has a much lower complexity and is computationally tractable. In the GAMP framework, the sparse signal and the observation are viewed to be generated according to some pre-specified probability distributions in the input and output channels. However, the parameters of the distributions are usually unknown in practice. In this paper, we propose an extended GAMP algorithm with built-in parameter estimation (PE-GAMP) and present its empirical convergence analysis. PE-GAMP treats the parameters as unknown random variables with simple priors and jointly estimates them with the sparse signals. Compared with Expectation Maximization (EM) based parameter estimation methods, the proposed PE-GAMP could draw information from the prior distributions of the parameters to perform parameter estimation. It is also more robust and much simpler, which enables us to consider more complex signal distributions apart from the usual Bernoulli-Gaussian (BGm) mixture distribution. Specifically, the formulations of Bernoulli-Exponential mixture (BEm) distribution and Laplace distribution are given in this paper. Simulated noiseless sparse signal recovery experiments demonstrate that the performance of the proposed PE-GAMP matches the oracle GAMP algorithm. When noise is present, both the simulated experiments and the real image recovery experiments show that PE-GAMP is still able to maintain its robustness and outperform EM based parameter estimation method when the sampling ratio is small. Additionally, using the BEm formulation of the PE-GAMP, we can successfully perform non-negative sparse coding of local image patches and provide useful features for the image classification task.
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