Semi-Supervised Learning with Variational Bayesian Inference and Maximum Uncertainty Regularization

Compressive sensing is a sub-Nyquist sampling technique for efficient signal acquisition and reconstruction of sparse or compressible signals. In order to account for the sparsity of the underlying signal of interest, it is common to use sparsifying priors such as Bernoulli–Gaussian-inverse Gamma (BGiG) and Gaussian-inverse Gamma (GiG) priors on the components of the signal. With the introduction of variational Bayesian inference, the sparse Bayesian learning (SBL) methods for solving the inverse problem of compressive sensing have received significant interest as the SBL methods become more efficient in terms of execution time. In this paper, we consider the sparse signal recovery problem using compressive sensing and the variational Bayesian (VB) inference framework. More specifically, we consider two widely used Bayesian models of BGiG and GiG for modeling the underlying sparse signal for this problem. Although these two models have been widely used for sparse recovery problems under various signal structures, the question of which model can outperform the other for sparse signal recovery under no specific structure has yet to be fully addressed under the VB inference setting. Here, we study these two models specifically under VB inference in detail, provide some motivating examples regarding the issues in signal reconstruction that may occur under each model, perform comparisons and provide suggestions on how to improve the performance of each model.

Existing studies on sparse Bayesian learning for structural damage detection usually assume that the posterior probability density functions follow standard distributions which facilitate to circumvent the intractable integration problem of the evidence by means of numerical sampling or analytical derivation. Moreover, the uncertainties of each mode are usually quantified as a common parameter to simplify the calculation. These assumptions may not be realistic in practice. This study proposes a sparse Bayesian method for structural damage detection suitable for standard and nonstandard probability distributions. The uncertainty corresponding to each mode is assumed as different. Variational Bayesian inference is developed and the posterior probability density functions of each unknown are individually derived. The parameters are found to follow the gamma distribution, whereas the distribution of the damage index cannot be directly obtained because of the nonlinear relationship in its posterior probability density function. The delayed rejection adaptive Metropolis algorithm is then adopted to generate numerical samples of the damage index. The coupled damage index and parameters in the variational Bayesian inference are successively calculated via an iterative process. A laboratory-tested frame is utilised to verify the effectiveness of the proposed method. The results indicate that the sparse damage can be accurately detected. The proposed method has the advantage of high accuracy and broad applicability.

Uncertainty propagation using infinite mixture of Gaussian processes and variational Bayesian inference

In this letter, we propose a novel ship detection method in synthetic aperture radar (SAR) imagery via variational Bayesian inference. First, we establish the ship detection probabilistic model which decomposes the SAR image as the sum of a sparse component associated with ships and a sea clutter component. Then, we introduce hierarchical priors of the latent variables in the model and use variational Bayesian inference to estimate the posterior distributions of the latent variables. The proposed method is an automatic iterative process without any sliding window. Experimental results accomplished over synthetic data and a RADARSAT-2 SAR image demonstrate that the proposed method can achieve state-of-the-art ship detection performance.

Many human genes express multiple transcript isoforms through alternative splicing, which greatly increases diversity of protein function. Although RNA sequencing (RNA-Seq) technologies have been widely used in measuring amounts of transcribed mRNA, accurate estimation of transcript isoform abundances from RNA-Seq data is challenging because reads often map to more than one transcript isoforms or paralogs whose sequences are similar to each other. We propose a statistical method to estimate transcript isoform abundances from RNA-Seq data. Our method can handle gapped alignments of reads against reference sequences so that it allows insertion or deletion errors within reads. The proposed method optimizes the number of transcript isoforms by variational Bayesian inference through an iterative procedure, and its convergence is guaranteed under a stopping criterion. On simulated datasets, our method outperformed the comparable quantification methods in inferring transcript isoform abundances, and at the same time its rate of convergence was faster than that of the expectation maximization algorithm. We also applied our method to RNA-Seq data of human cell line samples, and showed that our prediction result was more consistent among technical replicates than those of other methods. An implementation of our method is available at http://github.com/nariai/tigar nariai@megabank.tohoku.ac.jp Supplementary data are available at Bioinformatics online.

This letter addresses the recovery of hierarchical sparse signals in a Bayesian framework. Hierarchical sparse signals exhibit two levels of sparsity, i.e., block-sparsity among different blocks and internal sparsity within each individual block. As in sparse Bayesian learning, each component of the coefficient vector is firstly modeled as a Gaussian distributed variable with zero mean. To enforce the two-level hierarchical sparsity, the variance is further modeled by two classes of hidden variables controlling the block-sparsity and the internal sparsity, respectively. Finally, variational Bayesian inference is used to recover the coefficient vector from the noise corrupted data. Numerical simulation and experimental results show that the proposed method outperforms those recently reported recovery methods.

A low-complexity algorithm based on variational Bayesian inference for MIMO channel estimation

Cloud radio access network (C-RAN) is recognized as a key technology for the fifth generation (5G) wireless communication systems, where machine-type communication (MTC) is considered to support devices' connectivity. In this letter, we study the user activity detection (UAD) and channel estimation (CE) problems in C-RAN for MTC. Based on the user activity sparsity and signal spatial sparsity in C-RAN, we build a two-layer prior distribution graphical model to exploit the sparsity property and analyze the problem with variational Bayesian inference (VBI). We find that the width of prior distribution has a considerable impact on the algorithm performance and propose a modified VBI algorithm. Simulation results are presented to show that the proposed algorithm can achieve better performance with lower complexity than the existing approaches.

The paper proposes a new Kalman filtering (KF) algorithm called VBI-MCKF that combines the variational Bayesian inference (VBI)-based KF algorithm and the maximum correntropy KF (MCKF) for visual tracking problem. The VBI-based KF algorithm works to estimate the unknown measurement noise covariance matrix (MNCM) and process noise covariance matrix (PNCM), and the MCKF works to deal with non-Gaussian process noise and measurement noise. In order to cater for the visual tracking target scenario, where the MNCM and PNCM are unknown and non-Gaussian, we modify the VBI-based KF algorithm to work for suddenly occurring outliers and modify the MCKF work for small bandwidth. Simulations show that the proposed VBI-MCKF algorithm performs well when both covariance matrices of Gaussian process noise and non-Gaussian measurement noise are unknown or inaccurate.

Future mobile networks are projected to support integrated sensing and communications in high-speed communication scenarios. Nevertheless, large Doppler shifts induced by time-varying channels may cause severe inter-carrier interference (ICI). Frequency domain shows the potential of reducing ISAC complexity as compared with other domains. However, parameter mismatching issue still exists for such sensing. In this paper, we develop a novel sensing scheme based on sparse Bayesian framework, where the delay and Doppler estimation problem in time-varying channels is formulated as a 3D multiple measurement-sparse signal recovery (MM-SSR) problem. We then propose a novel two-layer variational Bayesian inference (VBI) method to decompose the 3D MM-SSR problem into two layers and estimate the Doppler in the first layer and the delay in the second layer alternatively. Subsequently, as is benefited from newly unveiled signal construction, a simplified two-stage multiple signal classification (MUSIC)-based VBI method is proposed, where the delay and the Doppler are estimated by MUSIC and VBI, respectively. Additionally, the Cramér-Rao bound (CRB) of the considered sensing parameters is derived to characterize the lower bound for the proposed estimators. Corroborated by extensive simulation results, our proposed method can achieve improved mean square error (MSE) than its conventional counterparts and is robust against the target number and target speed, thereby validating its wide applicability and advantages over prior arts.

Event-triggered state estimation has attracted significant attention due to the advantage of efficiently utilizing communication resources in wireless sensor networks. In this paper, an adaptive robust event-triggered variational Bayesian filtering method is designed for heavy-tailed noise with inaccurate nominal covariance matrices. The one-step state prediction probability density function and the measurement likelihood function are modeled as Student's t-distributions. By choosing inverse Wishart priors, the system state, the prediction error covariance, and the measurement noise covariance are jointly estimated based on the variational Bayesian inference and the fixed-point iteration. In the proposed filtering algorithm, the system states and the unknown covariances are adaptively updated by taking advantage of the event-triggered probabilistic information and the transmitted measurement data in the cases of non-transmission and transmission, respectively. The tracking simulations show that the proposed filtering method achieves good and robust estimation performance with low communication overhead.

A bi-partite generative model framework for analyzing and simulating large scale multiple discrete-continuous travel behaviour data

A probability model with Variational Bayesian Inference for the complex interference suppression in the acoustic array measurement

Orthogonal time frequency space (OTFS) is a new emerging modulation scheme that performs better than orthogonal frequency division multiplexing (OFDM) in high mobility scenarios. In this paper, we consider the delay-Doppler (DD) channel estimation problem in an OTFS system. By exploiting the inherent sparse nature of the DD channel, the channel estimation problem is modeled as a sparse signal recovery problem. Next, we build a two-layer graphical model with the Laplacian scale mixture (LSM) prior utilized to model the sparse channel. Then, a variational Bayesian inference (VBI) based algorithm is proposed to solve this problem. Simulation results are presented to show that the proposed algorithm can achieve better performance than other existing channel estimation algorithms.

To enhance the tracking accuracy of multi-ellipse extended target tracking for maneuvering targets, we propose a Variational Bayesian-based Interacting Multiple Model Maneuvering Extended Target Tracking Algorithm. The algorithm leverages multiple kinematic models within an Interacting Multiple Model framework to predict the target state, enabling better adaptation to various target kinematic modes during the time update. Following the prediction step, variational Bayesian inference, which includes inference of unknown measurement noise, is applied independently within each model to estimate the target’s position and shape. Then, model probabilities are updated based on the likelihood functions, and the model transition probabilities are adaptively learned. Concurrently, an ellipsoid fusion method is employed to combine the shape estimates from different models, while kinematic states are fused using model weights, yielding a robust overall target state estimate. The feasibility and performance of the proposed algorithm are validated by comparing its target tracking simulation results with those of other algorithms under different scenarios.