Sparse Bayesian Inference Research Articles

An enhanced direct position determination of non-circular sources via sparse Bayesian inference and grid refinement strategy

In this study, an off-grid sparse Bayesian inference (OGSBI) based direct position determination (DPD) algorithm is investigated. Existing SBI-based DPD algorithms are confronted with the challenge of excessive computational loads and lack of consideration for non-circular (NC) signals. To address these limitations, we present an enhanced OGSBI-based DPD algorithm for multiple non-circular sources. By utilizing the conjugate information of the NC signals, we expand the dimensionality of the data matrix to achieve a significant improvement in the localization performance. Additionally, a grid refinement strategy is developed to alleviate the computational loads, which involves an initial search to determine the approximate source locations, followed by fine localization using a denser grid. Moreover, the computational complexity and Cramér-Rao lower bound are derived to provide a comprehensive analysis of the proposed algorithm. Numerical simulations demonstrate the superiority of the proposed algorithm in terms of both localization accuracy and computational efficiency.

Sparse Bayesian inference with regularized Gaussian distributions *

Regularization is a common tool in variational inverse problems to impose assumptions on the parameters of the problem. One such assumption is sparsity, which is commonly promoted using lasso and total variation-like regularization. Although the solutions to many such regularized inverse problems can be considered as points of maximum probability of well-chosen posterior distributions, samples from these distributions are generally not sparse. In this paper, we present a framework for implicitly defining a probability distribution that combines the effects of sparsity imposing regularization with Gaussian distributions. Unlike continuous distributions, these implicit distributions can assign positive probability to sparse vectors. We study these regularized distributions for various regularization functions including total variation regularization and piecewise linear convex functions. We apply the developed theory to uncertainty quantification for Bayesian linear inverse problems and derive a Gibbs sampler for a Bayesian hierarchical model. To illustrate the difference between our sparsity-inducing framework and continuous distributions, we apply our framework to small-scale deblurring and computed tomography examples.

A fast asynchronous Markov chain Monte Carlo sampler for sparse Bayesian inference

Abstract We propose a very fast approximate Markov chain Monte Carlo sampling framework that is applicable to a large class of sparse Bayesian inference problems. The computational cost per iteration in several regression models is of order O(n(s+J)), where n is the sample size, s is the underlying sparsity of the model, and J is the size of a randomly selected subset of regressors. This cost can be further reduced by data sub-sampling when stochastic gradient Langevin dynamics are employed. The algorithm is an extension of the asynchronous Gibbs sampler of Johnson et al. [(2013). Analyzing Hogwild parallel Gaussian Gibbs sampling. In Proceedings of the 26th International Conference on Neural Information Processing Systems (NIPS’13) (Vol. 2, pp. 2715–2723)], but can be viewed from a statistical perspective as a form of Bayesian iterated sure independent screening [Fan, J., Samworth, R., & Wu, Y. (2009). Ultrahigh dimensional feature selection: Beyond the linear model. Journal of Machine Learning Research, 10, 2013–2038]. We show that in high-dimensional linear regression problems, the Markov chain generated by the proposed algorithm admits an invariant distribution that recovers correctly the main signal with high probability under some statistical assumptions. Furthermore, we show that its mixing time is at most linear in the number of regressors. We illustrate the algorithm with several models.

Research on High Robustness Underwater Target Estimation Method Based on Variational Sparse Bayesian Inference

Pulse noise (such as glacier fracturing and offshore pile driving), commonly seen in the marine environment, seriously affects the performance of Direction-of-Arrival (DOA) estimation methods in sonar systems. To address this issue, this paper proposes a high robustness underwater target estimation method based on variational sparse Bayesian inference by studying and analyzing the sparse prior assumption characteristics of signals. This method models pulse noise to build an observation signal, completes the derivation of the conditional distribution of the observed variables and the prior distribution of the sparse signals, and combines Variational Bayes (VB) theory to approximate the posterior distribution, thereby obtaining the recovered signal of the sparse signals and reducing the impact of pulse noise on the estimation system. Our simulation results showed that the proposed method achieved higher estimation accuracy than traditional methods in both single and multiple snapshot scenarios and has practical potential.

Super-resolution compressive spherical beamforming based on off-grid sparse Bayesian inference

Compressive spherical beamforming (CSB) with spherical microphone arrays is a panoramic acoustic source identification technology with high spatial resolution and clear acoustic imaging, which has broad application prospects. Due to the discretization of the focus region and the assumption of on-grid sources, classical CSB suffers from the basis mismatch problem, i.e., it faces performance deterioration when identifying off-grid sources. To overcome the problem, this paper proposes off-grid sparse Bayesian inference-based CSB (OGSBI-CSB). OGSBI-CSB formulates the direction of arrival (DOA) as the sum of the DOA of grid point and DOA offset, constructs an off-grid model based on Taylor expansion, and adapts OGSBI to solve the model and obtains DOA and strength estimation. Simulations and experiments demonstrate that the proposed OGSBI-CSB not only can effectively alleviate the basis mismatch problem and then improve identification accuracy for off-grid sources, but also enjoys super-resolution and good resistance to noise interference.

Saliency-Based SAR Target Detection via Convolutional Sparse Feature Enhancement and Bayesian Inference

Traditional synthetic aperture radar (SAR) target detection methods use matched filtered SAR images as input, and the detection performance is restricted due to the high sidelobes and speckle noise of these images. Sparse SAR imaging methods developed in recent years provide the advantages of reducing sidelobes, noise, and clutter. The imaging results obtained with these methods could help improve the SAR target detection performance. In this article, to improve the target detection performance using sparse SAR images as input, we proposed a convolutional sparse feature enhancement method to meet the needs of Bayesian saliency detection. The proposed Bayesian saliency joint target detection method comprised the following three steps: first, to obtain sparse SAR images with continuous contours and fewer holes in the target area, we proposed a convolutional L1 sparse regularization method. Second, a regularization parameter optimization method was derived to quickly obtain optimal regularization parameters for saliency detection. Finally, target detection results were obtained through a superpixel-based Bayesian saliency joint detector. Extensive experiments verified that the proposed method could improve the SAR target detection accuracy in complex backgrounds.

Joint Pilot Optimization, Target Detection and Channel Estimation for Integrated Sensing and Communication Systems

Radar sensing will be integrated into the 6G communication system to support various applications. In this integrated sensing and communication system, a radar target may also be a communication channel scatterer. In this case, the radar and communication channels exhibit certain joint burst sparsity. We propose a two-stage joint pilot optimization, target detection and channel estimation scheme to exploit such joint burst sparsity and pilot beamforming gain to enhance detection/estimation performance. In Stage 1, the base station (BS) sends downlink pilots (DP) for initial target search, and the user sends uplink pilots (UP) for channel estimation. Then the BS performs joint target detection and channel estimation. In Stage 2, the BS exploits the prior information obtained in Stage 1 to optimize the DP signal to further refine the performance. A Turbo Sparse Bayesian inference algorithm is proposed for joint target detection and channel estimation in both stages. The pilot optimization problem in Stage 2 is a semi-definite programming with rank-1 constraints. By replacing the rank-1 constraint with a tight and smooth approximation, we propose an efficient pilot optimization algorithm based on the majorization-minimization (MM) method. Simulations verify the advantages of the proposed scheme.

基于偏移全网格的离格稀疏贝叶斯推理的密集时延估计研究

基于偏移全网格的离格稀疏贝叶斯推理的密集时延估计研究

Grand Canonical Ensembles of Sparse Networks and Bayesian Inference.

Maximum entropy network ensembles have been very successful in modelling sparse network topologies and in solving challenging inference problems. However the sparse maximum entropy network models proposed so far have fixed number of nodes and are typically not exchangeable. Here we consider hierarchical models for exchangeable networks in the sparse limit, i.e., with the total number of links scaling linearly with the total number of nodes. The approach is grand canonical, i.e., the number of nodes of the network is not fixed a priori: it is finite but can be arbitrarily large. In this way the grand canonical network ensembles circumvent the difficulties in treating infinite sparse exchangeable networks which according to the Aldous-Hoover theorem must vanish. The approach can treat networks with given degree distribution or networks with given distribution of latent variables. When only a subgraph induced by a subset of nodes is known, this model allows a Bayesian estimation of the network size and the degree sequence (or the sequence of latent variables) of the entire network which can be used for network reconstruction.

Graph-based sparse bayesian broad learning system for semi-supervised learning

During the past decades, semi-supervised learning in classification has been regarded as one of the most active research area due to the increasing physical demand. Generally, the semi-supervised learning model believes the unlabeled data could potential be helpful to achieve higher performance as long as scare labeled samples under either cluster assumption or manifold assumption. However, most of the semi-supervised classifiers directly incorporate all the unlabeled data without any selective admission, which contains unfavorable features and noise diminishing performance while resulting in inability to large-scale data. In this paper, we propose a graph-based semi-supervised learning algorithm named GSB2LS within Bayesian framework for classification. The algorithm can explore unlabeled data effectively by adopting the compound prior that consists of unlabeled manifold information and sparse Bayesian inference to the broad structure. In particular, GSB2LS takes advantage of the broad structure to search for more potential associations of features, the manifold regularization to capture beneficial interdependence of unlabeled samples, the Bayesian framework to maintain the universal sparsity, the fast marginal likelihood maximization to update the relevance set based on the defined contribution, which leads to the feasibility to process large-scale data in the inductive way. Moreover, the algorithm is capable of outputting the probabilistic estimation of prediction for further decision analysis. Extensive empirical results verifies the excellent performance of our algorithm with clearly superior efficiency and generalization compared to other state-of-the-art semi-supervised classifiers.

Sparsifying priors for Bayesian uncertainty quantification in model discovery.

We propose a probabilistic model discovery method for identifying ordinary differential equations governing the dynamics of observed multivariate data. Our method is based on the sparse identification of nonlinear dynamics (SINDy) framework, where models are expressed as sparse linear combinations of pre-specified candidate functions. Promoting parsimony through sparsity leads to interpretable models that generalize to unknown data. Instead of targeting point estimates of the SINDy coefficients, we estimate these coefficients via sparse Bayesian inference. The resulting method, uncertainty quantification SINDy (UQ-SINDy), quantifies not only the uncertainty in the values of the SINDy coefficients due to observation errors and limited data, but also the probability of inclusion of each candidate function in the linear combination. UQ-SINDy promotes robustness against observation noise and limited data, interpretability (in terms of model selection and inclusion probabilities) and generalization capacity for out-of-sample forecast. Sparse inference for UQ-SINDy employs Markov chain Monte Carlo, and we explore two sparsifying priors: the spike and slab prior, and the regularized horseshoe prior. UQ-SINDy is shown to discover accurate models in the presence of noise and with orders-of-magnitude less data than current model discovery methods, thus providing a transformative method for real-world applications which have limited data.

Identification of dynamic mass-action biochemical reaction networks using sparse Bayesian methods.

Identifying the reactions that govern a dynamical biological system is a crucial but challenging task in systems biology. In this work, we present a data-driven method to infer the underlying biochemical reaction system governing a set of observed species concentrations over time. We formulate the problem as a regression over a large, but limited, mass-action constrained reaction space and utilize sparse Bayesian inference via the regularized horseshoe prior to produce robust, interpretable biochemical reaction networks, along with uncertainty estimates of parameters. The resulting systems of chemical reactions and posteriors inform the biologist of potentially several reaction systems that can be further investigated. We demonstrate the method on two examples of recovering the dynamics of an unknown reaction system, to illustrate the benefits of improved accuracy and information obtained.

Non-Circular Signals to Nested Array Via Sparse Bayesian Inference for Off-Grid Doa Estimation

Non-Circular Signals to Nested Array Via Sparse Bayesian Inference for Off-Grid Doa Estimation

Sparse Bayesian Inference-Based Direct Off-Grid Position Determination in Multipath Environments

The classical super-resolution Direct Position Determination (SR-DPD) algorithms fail to suppress the coherent Non-Line-of-Sight (NLOS) interference due to the lack of independent measurements. The existing Sparse Signal Reconstruction (SSR) based DPD approach suffers from the intractable complexity since it needs to solve a Second-Order Cone Programming (SOCP) problem. Besides, the Grid Quantization Error (GQE) exists in all above on-grid model based algorithms inherently. The proposed Sparse Bayesian Inference (SBI) based off-grid DPD algorithm is easy to implement as the Expectation-Maximization (EM) method is applied to decouple the multi-dimensional optimization problem. In addition, the GQE is also eliminated by introducing the Gradient Descent (GD) mechanism into the EM steps to update the grid point coordinates of interest iteratively.

Uncertainty quantification and reliability analysis by an adaptive sparse Bayesian inference based PCE model

An adaptive Bayesian polynomial chaos expansion (BPCE) is developed in this paper for uncertainty quantification (UQ) and reliability analysis. The sparsity in the PCE model is developed using automatic relevance determination (ARD) and the PCE coefficients are computed using the variational Bayesian (VB) inference. Further, Sobol sequence is utilized to evaluate a response quantity sequentially. Finally, leave one out (LOO) error is used to obtain the adaptive BPCE model. UQ and reliability analysis are performed of some numerical examples by the adaptive BPCE model. It is found that the optimal number of model evaluations and the optimal PCE degree are suitably selected simultaneously for a problem by the adaptive BPCE model. A highly accurate result is predicted by the proposed approach using very few model evaluation. Further, highly sparse PCE models are obtained by the ARD approach for most of the numerical examples. Additionally, distribution parameters of the predicted response quantity are also obtained by the VB inference, which are used to compute the confidence interval of the predicted response quantities.

Structural reliability analysis by a Bayesian sparse polynomial chaos expansion

Accurate computation of failure probability considering uncertain input parameters is very challenging within limited computational cost. An efficient surrogate model, referred to here as sparse variational Bayesian inference based polynomial chaos expansion (SVB-PCE), is formulated in this paper for reliability analysis. The sparsity in the polynomial basis terms is introduced by the automatic relevance determination (ARD) algorithm and the coefficients corresponding to the sparse polynomial bases are computed using the VB framework. The reliability analysis is performed on four typical numerical problems using the SVB-PCE model. The failure probability and the reliability index for all the examples are assessed accurately by the SVB-PCE model using fewer number of model evaluations as compared to the state-of-art methods. Further, the ARD enables to capture the most important terms in the polynomial bases which also reduces the computational cost in assessing the failure probability.

An Efficient Improved OGWSBI Algorithm for Accurate Off‐Grid DOA Estimation of Coherent Signals

The performance of the weighted sparse Bayesian inference (OGWSBI) algorithm for off‐grid coherent DOA estimation is not satisfactory due to the inaccurate weighting information. To increase the estimation accuracy and efficiency, an improved OGWSBI algorithm based on a higher‐order off‐grid model and unitary transformation for off‐grid coherent DOA estimation is proposed in this paper. Firstly, to reduce the approximate error of the first‐order off‐grid model, the steering vector is reformulated by the second‐order Taylor expansion. Then, the received data is transformed from complex value to real value and the coherent signals are decorrelated via utilizing unitary transformation, which can increase the computational efficiency and restore the rank of the covariance matrix. Finally, in the real field, the steering vector higher‐order approximation model and weighted sparse Bayesian inference are combined together to realize the estimation of DOA. Extensive simulation results indicate that under the condition of coherent signals and low SNR, the estimation accuracy of the proposed algorithm is about 50% higher than that of the OGWSBI algorithm, and the calculation time is reduced by about 60%.

Downward-Looking Linear Array Three-Dimensional SAR Imaging Based on the Two-Dimensional Mismatch Compensation

For downward-looking linear array (DLLA) three-dimensional (3-D) synthetic aperture radar (SAR), it is necessary to realize the super-resolution in both azimuth and cross-track direction due to the limited lengths of the synthetic aperture and the linear array. As all the scatterers are assumed on the uniform grids, the cross-track super-resolution can be achieved by 1-D compressed sensing. In the real imaging system, however, the gridding error should be considered because the biased scatterers lead to the mismatch of the measurement matrix and affect the imaging performance. The 1-D mismatch in cross-track direction has been solved by atomic norm minimization and off-grid sparse Bayesian inference. With the development of the super-resolution methods, the 2-D super-resolution in both azimuth and cross-track direction is realized by the 2-D compressed sensing (CS) algorithms. To solve the 2-D mismatch problem, a novel 2-D mismatch compensation method for DLLA 3-D SAR is proposed. Instead of converting the 2-D matrix signals to the 1-D vectors, the proposed method directly processes the 2-D mismatch with 2-D joint model. Furthermore, the 2-D joint model with 2-D mismatch is simplified as a normal sparse linear model, which is suitable for most of the CS reconstruction algorithms. It can not only provide better reconstruction performance but also reduce the memory cost and computation load. Finally, the simulation experiments are shown to demonstrate the validity of the proposed method.

An Off-Grid Block-Sparse Bayesian Method for Direction of Arrival and Polarization Estimation

The problem of DOA and polarization parameter estimation is considered in this paper from a perspective of sparse reconstruction. We present a novel off-grid hierarchical block-sparse Bayesian method for DOA and polarization parameter estimation to improve the estimation accuracy. Firstly, an off-grid model is formulated via the first-order Taylor expansion of the source steering vector. Then, a block-sparse vector is constructed based on sparse Bayesian inference, on which a two-layer hierarchical prior is imposed to promote block sparsity and internal sparsity simultaneously. Finally, the variables and model parameters are updated alternately by adopting the variational Bayesian approximation. In addition, the Cramer–Rao bound for DOA and polarization estimation, the convergence property and the computational complexity analysis of the proposed method are derived. Compared with the existing sparse reconstruction methods and the traditional subspace-based methods, the proposed method can achieve higher estimation accuracy. Simulation results demonstrate the effectiveness and notable performance of the proposed method.

Cloud-Assisted Cooperative Localization for Vehicle Platoons: A Turbo Approach

Due to the high resolution of angles of arrivals (AoAs) provided by the massive MIMO base station in 5 G wireless systems, it is promising to integrate 5G-based localization technology into autonomous driving to improve the accuracy and robustness of vehicle localization. In this paper, we investigate the problem of 5G cloud-assisted cooperative localization for vehicle platoons. The existing 5G-based localization algorithms focused on single-user localization and are not efficient for the localization of vehicle platoon where the positions of the vehicles are highly correlated. To the best of our knowledge, cloud-assisted cooperative localization tailored to vehicle platoons has not been studied before. To address this challenging problem, we first propose a Gamma-Markov-Group-Sparse (GMGS) model to capture the joint distribution of the vehicle positions in a vehicle platoon. Then we formulate the vehicle platoon cooperative localization as a sparse Bayesian inference (SBI) problem. The existing standard SBI algorithms such as variational Bayesian inference (VBI) and approximate message passing (AMP) cannot be applied to our platoon localization problem due to the complicated GMGS prior and the ill-conditioned measurement matrix. As such, we propose a novel turbo vehicle platoon cooperative localization (Turbo-VPCL) algorithm to fully exploit the correlations of the vehicle positions (as captured by the GMGS prior) under the ill-conditioned measurement matrix. Simulation results verify that the proposed Turbo-VPCL can achieve significant gain over the-state-of-art SBI algorithms.