Bayesian Learning Algorithm Research Articles

Coupling covariance matrix adaptation with continuum modeling for determination of kinetic parameters associated with electrochemical CO2 reduction

Coupling covariance matrix adaptation with continuum modeling for determination of kinetic parameters associated with electrochemical CO2 reduction

Deep Learning-Based Channel Estimation for Wideband Hybrid MmWave Massive MIMO

Hybrid analog-digital (HAD) architecture is widely adopted in practical millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems to reduce hardware cost and energy consumption. However, channel estimation in the context of HAD is challenging due to only limited radio frequency (RF) chains at transceivers. Although various compressive sensing (CS) algorithms have been developed to solve this problem by exploiting inherent channel sparsity and sparsity structures, practical effects, such as power leakage and beam squint, can still make the real channel features deviate from the assumed models and result in performance degradation. Besides, the high complexity of CS algorithms caused by a large number of iterations hinders their applications in practice. To tackle these issues, we develop a deep learning (DL)-based channel estimation approach where the sparse Bayesian learning (SBL) algorithm is unfolded into a deep neural network (DNN). In each SBL layer, Gaussian variance parameters of the sparse angular domain channel are updated by a tailored DNN, which is able to capture complicated channel sparsity structures in various domains effectively and efficiently. The measurement matrix is jointly optimized for performance improvement. Then, the proposed approach is extended to the multi-block case where channel correlation in time is further exploited to adaptively predict the measurement matrix and facilitate the update of variance parameters. Simulation results show that the proposed approaches outperform existing approaches in terms of both performance and complexity.

Robust Deep Learning for Uplink Channel Estimation in Cellular Network Under Inter-Cell Interference

Deep learning (DL)-based channel estimation has achieved remarkable success. However, most existing works focus on the white Gaussian noise which are inapplicable for cell-edge users under inter-cell interference (ICI). In this paper, we address this issue by proposing a novel DL-based channel estimation solution with a cascaded model-based and model-free deep neural network (DNN) structure. Specifically, the model-based module is designed by the variational Bayesian inference (VBI) technique to suppress the time-varying ICI, and the model-free module is designed by the Denoising Sparse Autoencoder (DSAE) structure to further refine the channel estimation. The proposed DNN is firstly pre-trained by offline supervised training, and various channel statistics are encapsulated in the DNN weights with the assist of a hyper-prior net modelling different sparse priors for different training samples. Then, an online Bayesian learning algorithm is proposed to train the model-based VBI module based on real-time pilot samples to track the online channel statistics. Simulation results verify that the proposed solution outperforms various state-of-the-art baseline schemes in a large SINR range with comparable performance to the estimator with genie-aided channel statistics.

Encoding nonlinear and unsteady aerodynamics of limit cycle oscillations using nonlinear sparse Bayesian learning

This article investigates the applicability of a recently proposed, nonlinear sparse Bayesian learning (NSBL) algorithm to identify and estimate the complex aerodynamics of limit cycle oscillations. NSBL provides a semi-analytical framework for determining the data-optimal sparse model nested within a (potentially) over-parameterized model. This is particularly relevant to nonlinear dynamical systems where modelling approaches involve the use of physics-based and data-driven components. In such cases, the data-driven components, where analytical descriptions of the physical processes are not readily available, are often prone to overfitting, meaning that the empirical aspects of these models will often involve the calibration of an unnecessarily large number of parameters. While an overparameterized model may fit the observed data well, such models may be inadequate for making predictions in regimes that are different from those wherein the data were recorded. In view of this, it is desirable to not only calibrate the model parameters, but also identify the optimal compromise between data fit and model complexity. In this article, we exhibit the optimal model discovery for an aeroelastic system wherein the structural dynamics are well-known and described by a differential equation model, coupled with a semi-empirical aerodynamic model for laminar separation flutter, resulting in low-amplitude limit cycle oscillations (LCO). To illustrate the performance of the algorithm, in this article, we use synthetic data and demonstrate the ability of the algorithm to correctly rediscover the optimal model and model parameters, given a known data-generating model. The synthetic data are generated from a forward simulation of a known differential equation model with parameters selected so as to mimic the dynamics observed in wind-tunnel experiments. Subsequently, we demonstrate the performance of the algorithm for model selection using noisy LCO data from wind tunnel experiments. As there is no ground truth available for the experimental data case, we provide a comparison between NSBL and Bayesian model selection to validate the results, and demonstrate the use of NSBL as an efficient alternative to traditional methods.

Fast estimation of direction of arrival based on sparse Bayesian learning for towed array sonar during manoeuvring

AbstractFor improving performance of the towed array sonar during the manoeuvring period, a processing framework is proposed based on joint estimation of direction of arrival (DOA) and the array shape. The sparse Bayesian learning (SBL) algorithm is utilised to accurately estimate the DOAs of interesting targets. Meanwhile, the towed array shape is modelled as a parabola array, and the array element positions are estimated using the bow of the parabola. Then, an approximate posterior covariance is implemented to the SBL for a fast converging speed required by practical applications. Besides, the co‐prime array structure is considered for the uniform linear array to further reduce the computational load. The numerical simulations have verified the effectiveness of the fast converging SBL method. MAPEX2000 experimental data processing results have shown that the proposed framework performs well in detection of weak targets during slow turns.

Sparse Bayesian Learning with hierarchical priors for duct mode identification of tonal noise

Fan noise has become an important noise component of civil aviation engines with the increasing bypass ratio. The mode identification method is the key to in-duct fan noise testing. The number of modes that can propagate through the duct increases dramatically for high-frequency in-duct fan noise, which requires a large number of microphones to measure the sound field in the duct. Since the number of modes is usually larger than the number of microphones, it is difficult to realize mode identification. A Sparse Bayesian Learning algorithm for mode identification is proposed to solve this problem in this paper. The in-duct sound field is described by a statistical model, and the inverse problem of mode identification is expressed in a Bayesian framework. The non-convex optimization problem of the cost function is considered, iteratively achieving the sparsest solution via a block coordinate descent algorithm in a majorization-minimization framework. The mode identification method based on Sparse Bayesian Learning has high sparsity and can achieve parameter adaptation. The effectiveness of the Sparse Bayesian Learning method for duct mode identification is verified by numerical simulations and experimental tests. The results show that the mode identification method of Sparse Bayesian Learning can accurately identify the target mode using fewer microphones.

Cegpy: Modelling with chain event graphs in Python

Chain event graphs (CEGs) are a recent family of probabilistic graphical models that generalise the popular Bayesian networks (BNs) family. Crucially, unlike BNs, a CEG is able to embed, within its graph and its statistical model, asymmetries exhibited by a process. These asymmetries might be in the conditional independence relationships or in the structure of the graph and its underlying event space. Structural asymmetries are common in many domains, and can occur naturally (e.g. a defendant vs prosecutor’s version of events) or by design (e.g. a public health intervention). Whilst two CEG packages exist in R for modelling processes with asymmetric conditional independencies, there currently exists no software that allows a user to leverage the theoretical developments of the CEG model family in modelling processes with structural asymmetries. In this paper, we present cegpy: the first Python implementation of CEGs and the first across all languages to support structurally asymmetric processes. cegpy contains an implementation of Bayesian learning and probability propagation algorithms for CEGs. We illustrate the functionality of cegpy using a structurally asymmetric dataset.

Diffusion equations with Markovian switching: Well-posedness, numerical generation and parameter inference

Complex systems in real world often experience abrupt changes or jumps that cannot be accurately captured by traditional partial differential equation modeling methods. However, the Markov switching model can effectively describe these abrupt system changes. To address this issue, it is essential to consider adopting the Markov switching model. In this paper, we propose a novel diffusion equation model with Markovian switching to represent the state jump phenomena of complex systems. We then establish the well-posedness property of this model and provide a numerical method with non-uniform grids to accurately simulate the solution of this mixture model with time-varying parameters. Moreover, a discrete sparse Bayesian learning algorithm are presented to estimate the diffusion equation’s parameters from spatiotemporal data with noise. Finally, we conduct several numerical simulation experiments to validate the effectiveness and precision of the proposed method. The results demonstrate that the Markov switching model is more adaptable than the traditional models for spatiotemporal data and can more accurately simulate the state jump phenomena of real-world systems.

Damage localization and robust diagnostics in guided-wave testing using multitask complex hierarchical sparse Bayesian learning

The inversion of guided-wave data for accurate damage localization is a challenging problem when using guided waves for nondestructive testing and robust diagnostics. It is especially important to detect incorrect damage localization without knowing the original damage. In this paper, a new damage localization and robust diagnostics method is proposed. A Multi-task Complex Hierarchical Sparse Bayesian learning (MuCHSBL) algorithm is presented to solve the inverse problem for damage localization based on the data measured from a small number of sensors. The multi-task model improves the efficacy of damage localization by utilizing the consistency of damage locations for tasks with different signal frequencies. A Sparse Bayesian learning algorithm is also introduced to utilize the spatial sparsity of the damage, since structural damage typically occurs at only a few localized areas. The quantified posterior uncertainty of the model parameters gives a sense of confidence in the damage localization results. Utilizing the different levels of uncertainty in the optimal and suboptimal inversion models, diagnostic tools are proposed to detect whether the inversion for damage localization is accurate, without knowing the original damage. Numerical and experimental studies are carried out to verify the effectiveness of the proposed method. It is demonstrated that the damage localization efficacy of multi-task model is much higher than that of single-task model; moreover, the accuracy of damage localization results can be diagnosed effectively by the posterior uncertainty quantification of the model parameters.

Joint AMP-SBL Algorithms for Device Activity Detection and Channel Estimation in Massive MIMO mMTC Systems

We consider the problem of detecting active devices and estimating their channels in the uplink of a massive machine type communication (mMTC) network. The base station (BS) in this mMTC system is equipped with massive multiple input multiple output (mMIMO) technology, and the channels across its antennas are correlated, an aspect ignored by most of the existing mMTC works. We propose three Bayesian learning algorithms which exploit channel spatial correlation, and comprehensively outperform several existing state-of-the-art algorithms, which do not exploit it. The proposed algorithms perform better in terms of the normalized mean squared error, activity error rate, and spectral efficiency (SE). The first correlated vector approximate message passing (AMP) algorithm has the best performance, but fails when the BS does not have knowledge of channel large scale fading and device activity probability. The second block sparse Bayesian learning (B-SBL) algorithm overcomes these limitations, but has a high complexity. The third combined AMP-BSBL algorithm retains the advantages of B-SBL, but with a much reduced complexity. We show that all three channel estimators can be represented as plug-in linear minimum mean squared estimators. This crucially helps us in deriving a common lower bound on the SE of mMIMO mMTC systems.

A Bayesian network structure learning method for optimizing ordering search operator

Local search algorithm in ordering space is a good method which can effectively improve the efficiency of bayesian network structure learning. However, the existing algorithms usually have problems such as insufficient order optimization, low learning accuracy, and easy stop at a local optimal. In order to solve these problems, the local search algorithm in ordering space is studied, and a new method to improve the accuracy of bayesian network structure learning by optimizing order search operator is proposed. Combining the iterative local search algorithm with the window operator to search the neighborhood of a given order in the ordering space, the probability of the algorithm falling into the local optimal value is reduced, and the network structure with higher quality is obtained. Experimental results show that comparing with the bayesian network structure learning algorithm in network structure space, the learning efficiency of the present algorithm is improved by 54.12%. Comparing with the bayesian network structure learning algorithm in ordering space, the learning accuracy of the present algorithm is improved by 2.33%.

Weighted sparse Bayesian method for direction of arrival estimation based on grid fission

AbstractAn off‐grid weighted sparse Bayesian learning algorithm based on grid fission for direction of arrival estimation is proposed. The existing grid fission algorithms can use fewer grid points with variant intervals to estimate the true DOAs. However, their learning processes are based on the traditional sparse Bayesian algorithm, which only assigns the same prior distribution assumption to the signals on all grids, but ignores the difference of signal distribution of different grid points. It will result in inaccurate fission location and fission direction because of the insufficient resolution of the spatial spectrum, reducing the estimation accuracy. Moreover, the fission strategy will cost much computation time due to the increase of grid points. To solve these problems, the proposed algorithm utilises the orthogonality of signal subspace and noise subspace to design the weights for prior signal distribution assumption, making the peaks of spatial spectrum more pronounced and easy to distinguish, using more accurate estimated DOAs and off‐grid parameter to determine the fission location and direction. In addition, the fission process deletes redundant grid points to simplify calculations. Compared with the existing grid fission algorithms, the proposed method has superior performance in estimation accuracy and computational time.

Score-based Bayesian network structure learning algorithms for modeling radioisotope levels in nuclear power plant reactors

Radioactive corrosion products released into the primary coolant loop dominate the final shutdown radiation fields of pressurized water reactors. Thus, reducing the concentration of these corrosion products is a paramount duty in the optimization process of the reactor performance. However, the complexity and uncertainty present in this process make it difficult to predict their evolution in a theoretical way. We propose the application of structural learning of Bayesian networks to discover the complex relations between the corrosion products and the most relevant variables in the primary loop, giving rise to probabilistic models that obtain accurate and reliable predictions of the corrosion products. Our analysis of 5 power plants demonstrates that our approach results in simpler and more reliable models. Additionally, we conclude that the learned structures may represent an interpretable tool for power plant technicians since they reveal useful information that can be directly employed to improve the reactor operation.

Minimizing the distortions in electrophysiological source imaging of cortical oscillatory activity via Spectral Structured Sparse Bayesian Learning.

Oscillatory processes at all spatial scales and on all frequencies underpin brain function. Electrophysiological Source Imaging (ESI) is the data-driven brain imaging modality that provides the inverse solutions to the source processes of the EEG, MEG, or ECoG data. This study aimed to carry out an ESI of the source cross-spectrum while controlling common distortions of the estimates. As with all ESI-related problems under realistic settings, the main obstacle we faced is a severely ill-conditioned and high-dimensional inverse problem. Therefore, we opted for Bayesian inverse solutions that posited a priori probabilities on the source process. Indeed, rigorously specifying both the likelihoods and a priori probabilities of the problem leads to the proper Bayesian inverse problem of cross-spectral matrices. These inverse solutions are our formal definition for cross-spectral ESI (cESI), which requires a priori of the source cross-spectrum to counter the severe ill-condition and high-dimensionality of matrices. However, inverse solutions for this problem were NP-hard to tackle or approximated within iterations with bad-conditioned matrices in the standard ESI setup. We introduce cESI with a joint a priori probability upon the source cross-spectrum to avoid these problems. cESI inverse solutions are low-dimensional ones for the set of random vector instances and not random matrices. We achieved cESI inverse solutions through the variational approximations via our Spectral Structured Sparse Bayesian Learning (ssSBL) algorithm https://github.com/CCC-members/Spectral-Structured-Sparse-Bayesian-Learning. We compared low-density EEG (10-20 system) ssSBL inverse solutions with reference cESIs for two experiments: (a) high-density MEG that were used to simulate EEG and (b) high-density macaque ECoG that were recorded simultaneously with EEG. The ssSBL resulted in two orders of magnitude with less distortion than the state-of-the-art ESI methods. Our cESI toolbox, including the ssSBL method, is available at https://github.com/CCC-members/BC-VARETA_Toolbox.

Inverse synthetic aperture radar autofocus imaging of block structure targets with sparse aperture

Inverse synthetic aperture radar (ISAR) autofocus imaging performance is challenged by the residual phase errors that arise from the traditional motion compensation methods with sparse aperture. Moreover, sparse reconstruction algorithms usually ignore the block sparsity in the ISAR image, which cannot recover structured information of the block structure target completely. An imaging method based on joint minimum Tsallis entropy and pattern-coupled sparse Bayesian learning algorithm is proposed to achieve ISAR autofocus imaging of block structure targets with sparse aperture. A pattern-coupled hierarchical complex Gaussian prior is utilized to characterize the correlation among ISAR image pixels in the complex domain. Such a prior model has the potential to encourage block-sparse patterns and achieve ISAR sparse aperture imaging of block structure targets without knowing the block partition prior information. The residual phase errors are estimated based on the minimum Tsallis entropy criterion during the sparse reconstruction of ISAR image to achieve ISAR autofocus imaging, which has the advantage of improving the computational efficiency compared with minimum Shannon entropy criterion. The superiority of the proposed algorithm is verified by the experimental results based on both simulated and measured data.

Retracted: Research on Moral Education Function of Music Art in College Students Based on Bayesian Learning Algorithm

Retracted: Research on Moral Education Function of Music Art in College Students Based on Bayesian Learning Algorithm

Short-Term Electrical Load Forecasting Based on Neural Networks

The article sets out the use of an artificial neural network for electrical load consumption forecasting. Electrical load prediction is one of the most demanded areas of research in the electric power industry. The two-layer artificial neural network of direct distribution with the number of neurons in the hidden layer equal to 6 was proposed in the article. The following data was taken as an input for forecasting short-term electrical load: electrical load, time, day of the week, temperature, day, weekend and working day code. According to the studies, the value of the mean absolute percentage error was 2.35, using the Bayesian Regularization learning algorithm.

Data poisoning attacks detection based on the convergence of the Peter and Clark algorithm and Bayesian adversarial federated learning

Effective Bayesian network structure learning algorithms, such as the Peter and Clark (PC) algorithm, must be designed and used with data integrity as a top priority. Deep learning models can be jointly built by thousands of participants; thanks to the innovative distributed learning technology known as federated learning. This research proposes a technique for the detection of data poisoning attacks along with enhancing secure data transmission and routing by utilizing the integration of the PC algorithm and federated learning. Data integrity of the network is likewise enhanced using the Convergence of the PC algorithm. Detection of attacks in established secure data transmission is carried out using Bayesian adversarial federated learning. We provided an optimization-based model poisoning approach and introduced adversarial neurons into the redundant area of a neural network by assessing model capacity. It should be highlighted that while those redundant neurons have little relevance to the primary goal of federated learning, they are crucial for poisoning attacks. Numerical tests show that the suggested approach can get beyond defense mechanisms and have a high attack success rate.

Probability-Based Diagnostic Imaging of Fatigue Damage in Carbon Fiber Composites Using Sparse Representation of Lamb Waves

Carbon fiber composites are commonly used in aerospace and other fields due to their excellent properties, and fatigue damage will occur in the process of service. Damage imaging can be performed using damage probability imaging methods to obtain the fatigue damage condition of carbon fiber composites. At present, the damage factor commonly used in the damage probability imaging algorithm has low contrast and poor anti-noise performance, which leads to artifacts in the imaging and misjudgment of the damaged area. Therefore, this paper proposes a fatigue damage probability imaging method for carbon fiber composite materials based on the sparse representation of Lamb wave signals. Based on constructing the Lamb wave dictionary, a fast block sparse Bayesian learning algorithm is used to represent the Lamb wave signals sparsely, and the definition of Lamb wave sparse representing the damage factor calculates the damage probability of the monitoring area and then images the fatigue damage of the carbon fiber composite materials. The imaging research was carried out using the fatigue monitoring experiment data of NASA’s carbon fiber composite materials. The results show that the proposed damage factor can clearly distinguish the damaged area from the undamaged area and has strong noise immunity. Compared with the energy damage factor and the cross-correlation damage factor, the error percentages are reduced by at least 58.63%, 28.11%, and 8.43% for signal-to-noise ratios of 6 dB, 3 dB, and 0.1 dB, respectively, after adding noise to the signal. The results can more accurately reflect the real location and area of fatigue damage in carbon fiber composites.

An efficient Bayesian network structure learning algorithm based on structural information

An efficient Bayesian network structure learning algorithm based on structural information