A variational Bayesian mixture modelling framework for cluster analysis of gene-expression data

We propose an application of variational Bayesian inference to the problem of blind estimation of single-input multiple-output (SIMO), finite-impulse-response (FIR) channels. The blind channel estimation problem has been extensively studied well over a decade. Nevertheless, there are some types of channel that cannot be successfully estimated by existing blind methods. One example of such a channel type is frequency-selective, exponentially-weighted Rayleigh fading channel. Our blind estimation approach to it is to incorporate prior knowledge on channel weighting in the form of channel prior distribution, then obtain the approximation to the posterior distribution of the channel using the variational Bayesian framework. Despite the error due to the mean field approximation involved in the variational framework, the derived algorithm has been verified by simulation to provide much improvements over the existing ones in a statistical sense.

Variational Bayesian inference based robust multiple measurement sparse signal recovery

Electromagnetic imaging of inhomogeneous objects is a nonlinear inverse scattering problem which can be effectively handled by means of linear inversion methods or nonlinear optimization methods. In addition to being nonlinear, inverse scattering problems are also ill-posed which can be overcome through a regularization scheme by taking into account some kind of a priori information. However, it is not straightforward to incorporate such inhomogeneity prior information into conventional inversion methods. In this work, we propose an innovative method to solve the problem of imaging inhomogeneous objects with piecewise homogeneity. Under Born approximation (BA), this problem is cast into a linear inversion one which is then addressed by means of a hierarchical Bayesian inversion method. To account for the piecewise homogeneity of the image, a Gaussian mixture model (GMM) is developed to enforce the feature. Specifically, a hidden label variable which is associated with each pixel is introduced for the class of materials and the contrast of each pixel is modeled as a mixture of independent Gaussian priors. Then, the proposed hierarchical Bayesian inversion method incorporates the GMM to the variational Bayesian inference framework to approximate the posterior distribution of all the unknowns (the unknown contrast, hidden label variable, and other model parameters). In addition, the damped generalized approximate message passing (GAMP) is utilized to circumvent the matrix inversion, making the overall process very computationally efficient. Extensive numerical examples will be shown to demonstrate the effectiveness of the proposed method.

BackgroundThe preoperative prediction of spread through air spaces (STAS) in patients with early-stage lung adenocarcinoma (LUAD) is crucial for selecting the appropriate surgical approach and improving patient outcomes. Previous research has confirmed that there is a significant correlation between consolidation-to-tumor ratio (CTR) and STAS. This study aimed to develop a Bayesian deep learning (DL) model based on the CTR prior to predict STAS in patients with stage IA LUAD.MethodsThis large-scale diagnostic study included patients with solitary primary invasive LUAD who underwent complete resection between November 2017 and October 2023. Enrolled patients were randomly assigned to training, validation, and test cohorts in a 7:2:1 ratio. Using a variational Bayesian inference framework, we developed a DL model based on the CTR prior (STAS-DLPrior CTR). The performance of STAS-DLPrior CTR was compared with another DL model without the CTR prior (STAS-DLNon-prior CTR) using the receiver operating characteristic (ROC) curve, calibration curve, decision curve analysis (DCA), and clinical impact curve (CIC).ResultsA total of 1,374 patients were included, with 961 in the training cohort, 275 in the validation cohort, and 138 in the test cohort. The results showed that CTR in the STAS-positive group was significantly higher than that in the STAS-negative group [0.63 (interquartile range, 0.36, 0.98) vs. 0.35 (interquartile range, 0.19, 0.60), P<0.001]. Compared to STAS-DLNon-prior CTR, the area under the ROC curve (AUC) tends to be higher for STAS-DLPrior CTR (0.831 vs. 0.731, P=0.06) in the validation cohort, and STAS-DLPrior CTR demonstrated a significantly higher AUC (0.858 vs. 0.637, P=0.008) in the test cohort. Additionally, the calibration curve suggested better calibration for STAS-DLPrior CTR. DCA and CIC also indicated that STAS-DLPrior CTR conferred higher clinical net benefit.ConclusionsThe proposed model based on the CTR prior offers significant advantages in predicting STAS in patients with stage IA LUAD, and incorporating doctors’ knowledge as priors can effectively guide the development of DL models.

The great success of deep learning (DL) has inspired researchers to develop more accurate and efficient symbol detectors for multi-input multi-output (MIMO) systems. Existing DL-based MIMO detectors, however, suffer several drawbacks. To address these issues, in this paper, we develop a model-driven DL detector based on variational Bayesian inference. Specifically, the proposed unrolled DL architecture is inspired by an inverse-free variational Bayesian learning framework which circumvents matrix inversion via maximizing a relaxed evidence lower bound. Two networks are respectively developed for independent and identically distributed (i.i.d.) Gaussian channels and arbitrarily correlated channels. The proposed networks, referred to as VBINet, have only a few learnable parameters and thus can be efficiently trained with a moderate amount of training samples. The proposed VBINet-based detectors can work in both offline and online training modes. An important advantage of our proposed networks over state-of-the-art MIMO detection networks such as OAMPNet and MMNet is that the VBINet can automatically learn the noise variance from data, thus yielding a significant performance improvement over the OAMPNet and MMNet in the presence of noise variance uncertainty. Simulation results show that the proposed VBINet-based detectors achieve competitive performance for both i.i.d. Gaussian and realistic 3GPP MIMO channels.

In this paper, we present a computer-aided follow-up (CAF) scheme to support physicians to track interval changes of pulmonary nodules on three dimensional (3D) CT images and to decide the treatment strategies without making any under or over treatment. Our scheme involves analyzing CT histograms to evaluate the volumetric distribution of CT values within pulmonary nodules. A variational Bayesian mixture modeling framework translates the image-derived features into an image-based risk score for predicting the patient recurrence-free survival. Through applying our scheme to follow-up 3D CT images of pulmonary nodules, we demonstrate the potential usefulness of the CAF scheme which can provide the trajectories that can characterize time interval changes of pulmonary nodules.

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.

The planar compound eye imaging system uses multiple sub-apertures to image the scene. Due to the constraint of the imaging sub-aperture size and spatial sampling rate of the image sensor, the image quality of each sub-aperture is low. How to fuse multiple sub-aperture images for a high-resolution image is an urgent problem. Multi-image super-resolution theory uses multiple images with complementary information to reconstruct high spatial resolution image. However, existing theories usually adopt the oversimplified motion model which is not suitable for planar compound eye imaging. If the existing multi-image super-resolution theory is directly applied to the resolution enhancement of the planar compound eye, the inaccurate motion estimation will reduce the performance of image resolution enhancement. In order to solve these problems, the motion model of the multi-image super-resolution is improved in the variational Bayesian framework, and the derived joint estimation algorithm is used to enhance the resolution of the planar compound eye. The correctness and effectiveness of the proposed method is verified by the simulation data experiments and the real compound eye data experiments.

Mitochondrial dysfunction is involved in many complex diseases. Efficient and accurate evaluation of mitochondrial functionality is crucial for understanding pathology as well as facilitating novel therapeutic developments. As a popular platform, Seahorse extracellular flux (XF) analyzer is widely used for measuring mitochondrial oxygen consumption rate (OCR) in living cells. A hidden feature of Seahorse XF OCR data is that it has a complex data structure, caused by nesting and crossing between measurement cycles, wells and plates. Surprisingly, statistical analysis of Seahorse XF data has not received sufficient attention, and current methods completely ignore the complex data structure, impairing the robustness of statistical inference. To rigorously incorporate the complex structure into data analysis, here we developed a Bayesian hierarchical modeling framework, OCRbayes, and demonstrated its applicability based on analysis of published data sets. We showed that OCRbayes can analyze Seahorse XF OCR experimental data derived from either single or multiple plates. Moreover, OCRbayes has potential to be used for diagnosing patients with mitochondrial diseases.

The conventional interacting multiple models (IMM) approach for a hybrid system under the Gaussian assumption is limited for most real applications due to the noisy measurements often being in the presence of outliers. This paper aims at accommodating the IMM approach to the non‐Gaussian cases where outliers exist. In the proposed IMM algorithm, the Student‐t distribution is used to model the non‐Gaussian measurement noise. At the interaction step, the mixed statistics of the noise parameter under a Bayesian framework are obtained via a Gamma approximation and a recently reported moments matching method. To address the state noise‐coupled intractability in Bayesian filtering, a variational Bayesian method is utilized to approximate the posterior distributions of the noise and state recursively. The proposed algorithm is tested with a maneuvering target tracking example and is shown to be robust to the outliers.

A novel unsupervised sparse component extraction algorithm is proposed for detecting micro defects while employing a thermography imaging system. The proposed approach is developed using the variational Bayesian framework. This enables a fully automated determination of the model parameters and bypasses the need for human intervention in manually selecting the appropriate image contrast frames. An internal subsparse grouping mechanism and adaptive fine-tuning strategy have been built to control the sparsity of the solution. The proposed algorithm is computationally affordable and yields a high-accuracy objective performance. Experimental tests on both artificial and natural defects have been conducted to verify the efficacy of the proposed method.

The highly accurate state estimation of nonlinear systems is needed in many different application fields. In many existing nonlinear filters, the uncompensated nonlinear approximation error and widely used numerical sampling methods both seriously affect the estimation accuracy and numerical stability. In this paper, based on the variational Bayesian framework, a novel iterative nonlinear filter consisting of forward modeling and inverse estimation is proposed. In the forward modeling stage, a linear Gaussian regression process with distributed variational parameters (VPs) is designed to fit the whole nonlinear measurement likelihood. The distributed VPs consider both first and second moments information, so as to compensate for approximation error from the whole likelihood perspective, instead of only the nonlinear function approximation, which can further improve the accuracy of Bayesian posterior update. In the linear Gaussian regression process, the original nonlinear measurement function (NMF) is just viewed as a prior and no longer directly participates in the modeling of the measurement likelihood. Hence, in the inverse estimation stage, when maximizing the evidence lower bound to update the posteriors of the state and VPs, we can obtain closed‐form solutions without numerical sampling methods to approximate the integral of NMF required in many existing methods, which can guarantee numerical stability. Moreover, to avoid the random setting of hyperparameters and to block the propagation of the accumulated error, we propose two rules, estimation and lower bound consistencies, to conduct the hyperparameters' initialization at the beginning of iteration at each sampling time and also derive an optimization method to update hyperparameters during iteration. Finally, the performance of our proposed method is demonstrated in the nonlinear orbital estimation problems.

In this paper we propose a new method for EEG source localization. Solving the above problem usually requires choosing an appropriate regularization term. Our method is based on the bayesian approach, hence, the regularization term is closely connected to the prior distribution. The proposed prior distribution has sparse properties favoring focal EEG sources. In order to obtain an efficient algorithm we use the Variational Bayesian framework which provides us a tractable iterative algorithm of closed form equations. We compare the proposed method with well-known approaches of EEG source localization and the results, using synthetic and real EEG data, have shown that our method presents state-of-the-art performance, especially in cases where we expect few activated brain regions.

A variational Bayesian based robust cubature Kalman filter under dynamic model mismatch and outliers interference

Publication in the conference proceedings of EUSIPCO, Lisbon, Portugal, 2014