Time-varying Dynamic Bayesian Networks Research Articles

Time-varying dynamic Bayesian network learning for an fMRI study of emotion processing.

This article presents a novel method for learning time-varying dynamic Bayesian networks. The proposed method breaks down the dynamic Bayesian network learning problem into a sequence of regression inference problems and tackles each problem using the Markov neighborhood regression technique. Notably, the method demonstrates scalability concerning data dimensionality, accommodates time-varying network structure, and naturally handles multi-subject data. The proposed method exhibits consistency and offers superior performance compared to existing methods in terms of estimation accuracy and computational efficiency, as supported by extensive numerical experiments. To showcase its effectiveness, we apply the proposed method to an fMRI study investigating the effective connectivity among various regions of interest (ROIs) during an emotion-processing task. Our findings reveal the pivotal role of the subcortical-cerebellum in emotion processing.

Online directed-structural change-point detection: A segment-wise time-varying dynamic Bayesian network approach

High-dimensional data streams exist in many applications. Generally these high-dimensional streaming data have complex directed conditional dependence relationships evolving over time. However, modeling their directed conditional dependence structure and detecting its change over time in an online way has not been well studied in the current literature. To that end, we propose an ONline Segment-wise tiMe-varying dynAmic Bayesian netwoRk model with exTernal information (ONSMART), together with an online score-based inferring algorithm for directed-structural change-point detection in high-dimensional data. ONSMART adopts a linear vector autoregressive (VAR) model to describe directed inter-slice and intra-slice relations of variables. It further takes additional information about similarities of variables into account and regularizes similar variables to have similar structure positions in the network with graph Laplacian. ONSMART allows the parameters of VAR to change segment-wisely over time to describe the evolution of the conditional dependence structure and adopts a customized pruned exact linear time algorithm framework to identify directed-structural change-point detection. The L-BFGS-B approach is embedded in this framework to obtain the optimal dependence structure for each segment. Numerical studies using synthetic data and real data from a three-phase flow system are performed to verify the effectiveness of ONSMART.

Segment-Wise Time-Varying Dynamic Bayesian Network with Graph Regularization

Time-varying dynamic Bayesian network (TVDBN) is essential for describing time-evolving directed conditional dependence structures in complex multivariate systems. In this article, we construct a TVDBN model, together with a score-based method for its structure learning. The model adopts a vector autoregressive (VAR) model to describe inter-slice and intra-slice relations between variables. By allowing VAR parameters to change segment-wisely over time, the time-varying dynamics of the network structure can be described. Furthermore, considering some external information can provide additional similarity information of variables. Graph Laplacian is further imposed to regularize similar nodes to have similar network structures. The regularized maximum a posterior estimation in the Bayesian inference framework is used as a score function for TVDBN structure evaluation, and the alternating direction method of multipliers (ADMM) with L-BFGS-B algorithm is used for optimal structure learning. Thorough simulation studies and a real case study are carried out to verify our proposed method’s efficacy and efficiency.

Information fusion architecture for secure cyber physical systems

The security essentially governs the usability and stability of Cyber Physical Systems (CPSs) whose cyber and physical components of the system are integrated. Security solutions to this effect are threefold - detecting attacks, preventing them and finally, maintaining system integrity under attacks. In this paper, we provide a solution to the problem of detecting collaborative attacks by proposing an information fusion architecture, which utilizes the strengths of Bayesian estimation in determining causalities as conditional probabilities. We propose a Time-Varying Dynamic Bayesian Network (TVDBN) to ascertain system state information, eventually enabling the system administrator to make control decisions and maintain system stability under security attacks. The control information to the physical components such as actuators is sent over by the sensors, which are the cyber components. As such, the focus of this paper is to provide a solution to uphold the stability of a CPS based on control theoretic aspects that can be adversely affected by compromised cyber components. Theoretical aspects touched in this paper for this purpose are - bounds on transmission delays, quantization errors and sampling time. Using our proposed information fusion architecture, we were able to detect the presence of both, the stand-alone and collaborative attacks on the CPS. Our experimental results showed that our fusion architecture can detect collaborative attacks and profile them with an average accuracy of 91.7%. Given the difficulty in detecting the presence of collaborative attacks in CPS, this level of accuracy is considered high to protect CPS applications.

The design of a cloud-based tracker platform based on system-of-systems service architecture

Devices embedded with position tracking facilities are now widely available, such as smartphones, smartwatches, vehicle location trackers, etc. However, data mining and advanced analytics are rarely bundled with these devices that limits their utility. In this paper, we present the design of a generic, programmable position tracking platform, namely CQtracker. In particular, this platform is incorporated with a cloud-based engine of advanced analytics. CQtracker is constructed based on a concept of system-of-systems service architecture to deliver data-system-as-a-service. It is designed for the consumption by a variety of spatio-temporal applications. Spatio-temporal data exhibit strong heterogeneous patterns, data sparseness and distribution skewness. Hence, they are difficult to analyze. CQtracker reveals relationships and structures from these data by self-regularized time-varying dynamic Bayesian networks. In addition, a Bayesian parameter estimation approach is applied to an epidemic model for outbreak predictions. Sample applications are presented in this paper, in which CQtracker successfully reveals the evolution of time-varying structures from traffic trajectories.

Cortical subnetwork dynamics during human language tasks

Language tasks require the coordinated activation of multiple subnetworks—groups of related cortical interactions involved in specific components of task processing. Although electrocorticography (ECoG) has sufficient temporal and spatial resolution to capture the dynamics of event-related interactions between cortical sites, it is difficult to decompose these complex spatiotemporal patterns into functionally discrete subnetworks without explicit knowledge of each subnetwork's timing. We hypothesized that subnetworks corresponding to distinct components of task-related processing could be identified as groups of interactions with co-varying strengths. In this study, five subjects implanted with ECoG grids over language areas performed word repetition and picture naming. We estimated the interaction strength between each pair of electrodes during each task using a time-varying dynamic Bayesian network (tvDBN) model constructed from the power of high gamma (70–110Hz) activity, a surrogate for population firing rates. We then reduced the dimensionality of this model using principal component analysis (PCA) to identify groups of interactions with co-varying strengths, which we term functional network components (FNCs). This data-driven technique estimates both the weight of each interaction's contribution to a particular subnetwork, and the temporal profile of each subnetwork's activation during the task. We found FNCs with temporal and anatomical features consistent with articulatory preparation in both tasks, and with auditory and visual processing in the word repetition and picture naming tasks, respectively. These FNCs were highly consistent between subjects with similar electrode placement, and were robust enough to be characterized in single trials. Furthermore, the interaction patterns uncovered by FNC analysis correlated well with recent literature suggesting important functional-anatomical distinctions between processing external and self-produced speech. Our results demonstrate that subnetwork decomposition of event-related cortical interactions is a powerful paradigm for interpreting the rich dynamics of large-scale, distributed cortical networks during human cognitive tasks.

Time-varying dynamic Bayesian network model and its application to brain connectivity using electrocorticograph

Cortical networks for speech production are believed to be widely distributed and highly organized over temporal, parietal, and frontal lobes areas in the human brain cortex. Effective connectivity demonstrates an inherent element of directional information propagation, and is therefore an information dense measure for the relevant activity over different cortical regions. Connectivity analysis of electrocorticographic (ECoG) recordings has been widely studied for its excellent signal-to-noise ratio as well as high temporal and spatial resolutions, providing an important approach to human electrophysiological researches. In this paper, we evaluate two patients undergoing invasive monitoring for seizure localization, in which both micro-electrode and standard clinical electrodes are used for ECoG recordings from speech-related cortical areas during syllable reading test. In order to explore the dynamics of speech processing, we extract the high gamma frequency band (70-110 Hz) power from ECoG signals by the multi-taper method. The trial-averaged results show that there is a consistent task-related increase in high gamma response for micro-ECoG electrodes for patient 1 and standard-ECoG electrodes for both patients 1 and 2. We demonstrate that high gamma response provides reliable speech localization compared with electrocortical stimulation. In addition, a directed connectivity network is built in single trial involving both standard ECoG electrodes and micro-ECoG arrays using time-varying dynamic Bayesian networks (TV-DBN). The TV-DBN is used to model the time-varying effective connectivity between pairs of ECoG electrodes selected by high gamma power, with less parameter optimization required and higher computational simplicity than short-time direct directed transfer function. We observe task-related connectivity modulations of connectivity between large-scale cortical networks (standard ECoG) and local cortical networks (micro-ECoG), as well as between large-scale and local cortical networks. In addition, cortical connectivity is modulated differently before and after response articulation onset. In other words, electrodes located over sensorimotor cortex show higher connectivity before articulation onset, while connectivity appears gradually between sensorimotor and auditory cortex after articulation onset. Also, the connectivity patterns observed during articulation are significantly different for three different places of articulation for the consonants. This study offers insights into preoperative evaluation during epilepsy surgery, dynamic real-time brain connectivity visualization, and assistance to understand the dynamic processing of language pronunciation in the language cortex.

Self-regularized causal structure discovery for trajectory-based networks

Trajectory-based networks exhibit strong heterogeneous patterns amid human behaviors. We propose a notion of causal time-varying dynamic Bayesian network (cTVDBN) to efficiently discover such patterns. While asymmetric kernels are used to make the model better adherence to causal principles, the variations of network connectivities are addressed by an adaptive over-fitting control. Compact regularization paths are obtained by approximate homotopy to make the solution tractable. In our experiments, cTVDBN structure discovery has successfully revealed the evolution of time-varying relationships in a ring road system, and provided insights for plausible road structure improvements from a traffic flow dataset.

Inferring dynamic gene regulatory networks in cardiac differentiation through the integration of multi-dimensional data.

BackgroundDecoding the temporal control of gene expression patterns is key to the understanding of the complex mechanisms that govern developmental decisions during heart development. High-throughput methods have been employed to systematically study the dynamic and coordinated nature of cardiac differentiation at the global level with multiple dimensions. Therefore, there is a pressing need to develop a systems approach to integrate these data from individual studies and infer the dynamic regulatory networks in an unbiased fashion.ResultsWe developed a two-step strategy to integrate data from (1) temporal RNA-seq, (2) temporal histone modification ChIP-seq, (3) transcription factor (TF) ChIP-seq and (4) gene perturbation experiments to reconstruct the dynamic network during heart development. First, we trained a logistic regression model to predict the probability (LR score) of any base being bound by 543 TFs with known positional weight matrices. Second, four dimensions of data were combined using a time-varying dynamic Bayesian network model to infer the dynamic networks at four developmental stages in the mouse [mouse embryonic stem cells (ESCs), mesoderm (MES), cardiac progenitors (CP) and cardiomyocytes (CM)]. Our method not only infers the time-varying networks between different stages of heart development, but it also identifies the TF binding sites associated with promoter or enhancers of downstream genes.The LR scores of experimentally verified ESCs and heart enhancers were significantly higher than random regions (p <10−100), suggesting that a high LR score is a reliable indicator for functional TF binding sites. Our network inference model identified a region with an elevated LR score approximately −9400 bp upstream of the transcriptional start site of Nkx2-5, which overlapped with a previously reported enhancer region (−9435 to −8922 bp). TFs such as Tead1, Gata4, Msx2, and Tgif1 were predicted to bind to this region and participate in the regulation of Nkx2-5 gene expression. Our model also predicted the key regulatory networks for the ESC-MES, MES-CP and CP-CM transitions.ConclusionWe report a novel method to systematically integrate multi-dimensional -omics data and reconstruct the gene regulatory networks. This method will allow one to rapidly determine the cis-modules that regulate key genes during cardiac differentiation.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-015-0460-0) contains supplementary material, which is available to authorized users.

A Non-Homogeneous Dynamic Bayesian Network with Sequentially Coupled Interaction Parameters for Applications in Systems and Synthetic Biology

An important and challenging problem in systems biology is the inference of gene regulatory networks from short non-stationary time series of transcriptional profiles. A popular approach that has been widely applied to this end is based on dynamic Bayesian networks (DBNs), although traditional homogeneous DBNs fail to model the non-stationarity and time-varying nature of the gene regulatory processes. Various authors have therefore recently proposed combining DBNs with multiple changepoint processes to obtain time varying dynamic Bayesian networks (TV-DBNs). However, TV-DBNs are not without problems. Gene expression time series are typically short, which leaves the model over-flexible, leading to over-fitting or inflated inference uncertainty. In the present paper, we introduce a Bayesian regularization scheme that addresses this difficulty. Our approach is based on the rationale that changes in gene regulatory processes appear gradually during an organism's life cycle or in response to a changing environment, and we have integrated this notion in the prior distribution of the TV-DBN parameters. We have extensively tested our regularized TV-DBN model on synthetic data, in which we have simulated short non-homogeneous time series produced from a system subject to gradual change. We have then applied our method to real-world gene expression time series, measured during the life cycle of Drosophila melanogaster, under artificially generated constant light condition in Arabidopsis thaliana, and from a synthetically designed strain of Saccharomyces cerevisiae exposed to a changing environment.

Connectivity Analysis as a Novel Approach to Motor Decoding for Prosthesis Control

The use of neural signals for prosthesis control is an emerging frontier of research to restore lost function to amputees and the paralyzed. Electrocorticography (ECoG) brain-machine interfaces (BMI) are an alternative to EEG and neural spiking and local field potential BMI approaches. Conventional ECoG BMIs rely on spectral analysis at specific electrode sites to extract signals for controlling prostheses. We compare traditional features with information about the connectivity of an ECoG electrode network. We use time-varying dynamic Bayesian networks (TV-DBN) to determine connectivity between ECoG channels in humans during a motor task. We show that, on average, TV-DBN connectivity decreases from baseline preceding movement and then becomes negative, indicating an alteration in the phase relationship between electrode pairs. In some subjects, this change occurs preceding and during movement, before changes in low or high frequency power. We tested TV-DBN output in a hand kinematic decoder and obtained an average correlation coefficient (r(2)) between actual and predicted joint angle of 0.40, and as high as 0.66 in one subject. This result compares favorably with spectral feature decoders, for which the average correlation coefficient was 0.13. This work introduces a new feature set based on connectivity and demonstrates its potential to improve ECoG BMI accuracy.

Time Varying Dynamic Bayesian Network for Nonstationary Events Modeling and Online Inference

This paper presents a novel time varying dynamic Bayesian network (TVDBN) model for the analysis of nonstationary sequences which are of interest in many fields. The changing network structure and parameter in TVDBN are treated as random processes whose values at each time epoch determine a stationary DBN model; this DBN model is then used to specify the distribution of data sequence at the time epoch. Under such a hierarchical formulation, the changing state of network can be incorporated into the Bayesian framework straightforwardly. The network state is assumed to transit smoothly in the joint space of numerical parameter and graphical topology so that we can achieve robust online network learning even without abundant observations. Particle filtering is employed to dynamically update current network state as well as infer hidden data values. We implement our time varying model for data sequences of multinomial and Gaussian distributions, while the general model framework can be used for any other distribution. Simulations on synthetic data and evaluations on video sequences both demonstrate that the proposed TVDBN is effective in modeling nonstationary sequences. Comprehensive comparisons have been made against existing nonstationary models, and our proposed model is shown to be the top performer.

Connectivity analysis as a novel approach to motor decoding for prosthesis control

The use of neural signals for prosthesis control is an emerging frontier of research to restore lost function to amputees and the paralyzed. Electrocorticography (ECoG) brain-machine interfaces (BMI) are an alternative to EEG and neural spiking and local field potential BMI approaches. Conventional ECoG BMIs rely on spectral analysis at specific electrode sites to extract signals for controlling prostheses. We compare traditional features with information about the connectivity of an ECoG electrode network. We use time-varying dynamic Bayesian networks (TV-DBN) to determine connectivity between ECoG channels in humans during a motor task. We show that, on average, TV-DBN connectivity decreases from baseline preceding movement and then becomes negative, indicating an alteration in the phase relationship between electrode pairs. In some subjects, this change occurs preceding and during movement, before changes in low or high frequency power. We tested TV-DBN output in a hand kinematic decoder and obtained an average correlation coefficient (r2) between actual and predicted joint angle of 0.40, and as high as 0.66 in one subject. This result compares favorably with spectral feature decoders, for which the average correlation coefficient was 0.13. This work introduces a new feature set based on connectivity and demonstrates its potential to improve ECoG BMI accuracy.

Dynamic gene network reconstruction from gene expression data in mice after influenza A (H1N1) infection

BackgroundThe immune response to viral infection is a temporal process, represented by a dynamic and complex network of gene and protein interactions. Here, we present a reverse engineering strategy aimed at capturing the temporal evolution of the underlying Gene Regulatory Networks (GRN). The proposed approach will be an enabling step towards comprehending the dynamic behavior of gene regulation circuitry and mapping the network structure transitions in response to pathogen stimuli.ResultsWe applied the Time Varying Dynamic Bayesian Network (TV-DBN) method for reconstructing the gene regulatory interactions based on time series gene expression data for the mouse C57BL/6J inbred strain after infection with influenza A H1N1 (PR8) virus. Initially, 3500 differentially expressed genes were clustered with the use of k-means algorithm. Next, the successive in time GRNs were built over the expression profiles of cluster centroids. Finally, the identified GRNs were examined with several topological metrics and available protein-protein and protein-DNA interaction data, transcription factor and KEGG pathway data.ConclusionsOur results elucidate the potential of TV-DBN approach in providing valuable insights into the temporal rewiring of the lung transcriptome in response to H1N1 virus.