Compressed Sensing (CS) is an effective technique to recover sparse signals with fewer samples than what is required by the classical Shannon Nyquist sampling theorem. The sensing matrix, sparsifying transform, and sparse recovery algorithm are three key factors for accurate reconstruction in CS. Traditional CS uses a convex $l_{1}$-norm sparse regularizer which may lead to biased estimates and is suboptimal in promoting sparsity. Another challenge is the design of incoherent sensing matrices which is crucial for accurate sparse recovery. In this paper, we propose a novel CS framework combining a preconditioned sensing matrix and nonconvex regularization for improved sparse signal recovery. First, we formulate an optimization problem to find an incoherent sensing matrix via a preconditioner. It allows for a direct computation of the optimal preconditioner and preconditioned sensing matrix, simultaneously. Secondly, we consider a generalized CS model for signal recovery based on the incoherent sensing matrix and a nonconvex $\ell _{1/2}$-norm regularizer. We then derive an Alternating Direction Method of Multipliers (ADMM) algorithm to solve this nonconvex optimization problem. The proposed model is applied to sparse-view Computed Tomography (CT) reconstruction with highly-undersampled and noisy data. Qualitative and quantitative results show significantly better image reconstruction using the preconditioned sensing matrix and $\ell _{1/2}$ regularizer, compared to methods without preconditioning and using the $\ell _{1}$ regularizer.

Interpretable classification of time series poses significant challenges in high dimensions. Traditional feature selection methods in the frequency domain often assume sparsity in spectral matrices (or their inverses) which can be restrictive for real-world applications. We propose a model-based approach for classifying high-dimensional stationary time series by assuming sparsity in the difference between spectra. The estimators for the model parameters are proven to be consistent under general conditions. We also introduce a method to select the most discriminatory frequencies, and it possesses the sure screening property. The novelty of our method lies in the interpretability of the parameters hence suitable for neuroscience where understanding differences in brain network connectivity across various states is crucial. The proposed approach is tested using several simulated examples and applied to EEG and calcium imaging datasets to demonstrate its practical relevance.

Understanding the evolving dependence between two sets of multivariate signals is fundamental in neuroscience and other domains where sub-networks in a system interact dynamically over time. Despite the growing interest in multivariate time series analysis, existing methods for between-clusters dependence typically rely on the assumption of stationarity and lack the temporal resolution to capture transient, frequency-specific interactions. To overcome this limitation, we propose scale-specific wavelet canonical coherence (WaveCanCoh), a novel framework that extends canonical coherence analysis to the nonstationary setting by leveraging the multivariate locally stationary wavelet model. The proposed WaveCanCoh enables the estimation of time-varying canonical coherence between clusters, providing interpretable insight into scale-specific time-varying interactions between clusters. Through extensive simulation studies, we demonstrate that WaveCanCoh accurately recovers true coherence structures under both locally stationary and general nonstationary conditions. Application to local field potential (LFP) activity data recorded from the hippocampus reveals distinct dynamic coherence patterns between correct and incorrect memory-guided decisions, illustrating capacity of the method to detect behaviorally relevant neural coordination. These results highlight WaveCanCoh as a flexible and principled tool for modeling complex cross-group dependencies in nonstationary multivariate systems. Code for implementing WaveCanCoh is available at https://github.com/mhaibo/WaveCanCoh.git.

Electroencephalography (EEG) is a non-invasive tool widely used for studying brain activity, offering high temporal resolution for real-time analysis of neural dynamics. This study investigates the neurophysiological underpinnings of Attention Deficit Hyperactivity Disorder (ADHD) through statistical spectral and coherence analysis of EEG data. By focusing on frequency bands, we identified distinct patterns in ADHD subjects, including increased beta and alpha power, reduced gamma activity, and altered connectivity in key brain regions. These findings underscore the potential of EEG-based biomarkers for improving ADHD diagnosis and treatment strategies.

Brain functional connectivity (FC) changes are associated with neuropsychiatric disorders and other underlying factors, such as age and gender. Due to small training sample, data augmentation has been increasingly used for deep learning-based classification of brain FC. Although deep generative models could generate brain FCs to enhance downstream classification, most existing methods neglect the underlying factors involved in the generation process and fail to preserve the subject identity. We propose a novel brain FC conditional Generative Adversarial Network (GAN) called BrainFC-CGAN with specialized layers and filters to preserve the symmetry property and topological structure of brain FCs. We design a FC generator that captures the complex variations between brain FCs, ages, and health statuses to generate synthetic FCs that preserve the subject identity. We categorized true brain FCs into different age groups; an augmented age-specific dataset generated from BrainFC-CGAN is combined with the training set for classification. Experimental results on major depressive disorder (MDD) resting-state functional magnetic resonance imaging data show that the proposed method synthesizes realistic brain FCs of different target age groups, significantly improving downstream classification performance over baseline without augmentation, and also outperforming several state-of-the-art GANs.

Analyzing the community structure of brain networks provides new insights into human brain function. Existing studies broadly use conventional network clustering approaches. While graph neural networks have recently shown promise in modeling brain functional connectivity (FC) networks, their applications to brain community detection still need improvement and further refinement. Moreover, identifying common community structure while resolving the single-subject partitions across multiple individual networks remains underexplored. We propose a Deep Multi-Graph Embedded Clustering (DMGEC) framework to identify shared community partition in brain FC networks over a cohort of individuals. By incorporating the consensus information aggregated across network structures, DMGEC leverages a graph autoencoder to produce consensus-aware latent representations of individual networks, and applies deep embedded clustering on the multi-subject network representation to produce common community assignment of brain nodes. Simulations show superior community recovery by our method compared to conventional approaches, especially for networks with large number of communities. When applied to functional magnetic resonance imaging (fMRI) data, the DMGEC achieves outstanding alikeness over individual partitions, and uncovers group-level differences in brain community motifs between major depressive disorder patients and normal controls.

Compressed sensing (CS) exploiting inherent sparsity prior of signals has been proven effective for sparse-view computed tomography (CT) image reconstruction from undersampled projection data. However, most CS-based CT studies focused on formulating different sparsity regularizers, e.g., total variation (TV) minimization, and neglect design of an incoherent sensing matrix - a key factor of CS performance. The sensing matrix formed by an incomplete set of Radon projections in CT typically exhibits large coherence. In this paper, we propose a novel method for optimizing the sensing matrix via preconditioning to improve CS-CT reconstruction. A well-conditioned preconditioner is designed to optimally reduce the coherence of the sensing matrix and thus improving the CS systems. The desired preconditioner is obtained by solving a nonconvex optimization problem via gradient descent method. The preconditioned systems solved by TV-based sparse recovery algorithms can provide better reconstruction accuracy with fewer measurements even in noisy settings. Evaluated on brain and COVID-19 chest CT datasets, the proposed method when used for preconditioning of Radon sensing matrix reconstructed images with substantially higher quality with faster speed than baselines without preconditioning.

The low-rank plus sparse (L+S) decomposition model has enabled better reconstruction of dynamic magnetic resonance imaging (dMRI) with separation into background (L) and dynamic (S) component. However, use of low-rank prior alone may not fully explain the slow variations or smoothness of the background part at the local scale. In this paper, we propose a smoothness-regularized L+S (SR-L+S) model for dMRI reconstruction from highly undersampled k-t-space data. We exploit joint low-rank and smooth priors on the background component of dMRI to better capture both its global and local temporal correlated structures. Extending the L+S formulation, the low-rank property is encoded by the nuclear norm, while the smoothness by a general $\ell_{p}$-norm penalty on the local differences of the columns of L. The additional smoothness regularizer can promote piecewise local consistency between neighboring frames. By smoothing out the noise and dynamic activities, it allows accurate recovery of the background part, and subsequently more robust dMRI reconstruction. Extensive experiments on multi-coil cardiac and synthetic data shows that the SR-L+S model outperforms several state-of-the-art methods in terms of recovery accuracy.

MOTIVATION: Identifying causal relations between diseases allows for the study of shared pathways, biological mechanisms, and inter-disease risks. Such causal relations can facilitate the identification of potential disease precursors and candidates for drug re-purposing. However, computational methods often lack access to these causal relations. Few approaches have been developed to automatically extract causal relationships between diseases from unstructured text, but they are often only focused on a small number of diseases, lack validation of the extracted causal relations, or do not make their data available. RESULTS: We automatically mined statements asserting a causal relation between diseases from the scientific literature by leveraging lexical patterns. Following automated mining of causal relations, we mapped the diseases to the International Classification of Diseases (ICD) identifiers to allow the direct application to clinical data. We provide quantitative and qualitative measures to evaluate the mined causal relations and compare to UK Biobank diagnosis data as a completely independent data source. The validated causal associations were used to create a directed acyclic graph that can be used by causal inference frameworks. We demonstrate the utility of our causal network by performing causal inference using the do-calculus, using relations within the graph to construct and improve polygenic risk scores, and disentangle the pleiotropic effects of variants. AVAILABILITY AND IMPLEMENTATION: The data are available through https://github.com/bio-ontology-research-group/causal-relations-between-diseases.

Brain functional connectivity (FC) networks inferred from functional magnetic resonance imaging (fMRI) have shown altered or aberrant brain functional connectome in various neuropsychiatric disorders. Recent application of deep neural networks to connectome-based classification mostly relies on traditional convolutional neural networks (CNNs) using input FCs on a regular Euclidean grid to learn spatial maps of brain networks neglecting the topological information of the brain networks, leading to potentially sub-optimal performance in brain disorder identification. We propose a novel graph deep learning framework that leverages non-Euclidean information inherent in the graph structure for classifying brain networks in major depressive disorder (MDD). We introduce a novel graph autoencoder (GAE) architecture, built upon graph convolutional networks (GCNs), to embed the topological structure and node content of large fMRI networks into low-dimensional representations. For constructing the brain networks, we employ the Ledoit-Wolf (LDW) shrinkage method to efficiently estimate high-dimensional FC metrics from fMRI data. We explore both supervised and unsupervised techniques for graph embedding learning. The resulting embeddings serve as feature inputs for a deep fully-connected neural network (FCNN) to distinguish MDD from healthy controls (HCs). Evaluating our model on resting-state fMRI MDD dataset, we observe that the GAE-FCNN outperforms several state-of-the-art methods for brain connectome classification, achieving the highest accuracy when using LDW-FC edges as node features. The graph embeddings of fMRI FC networks also reveal significant group differences between MDD and HCs. Our framework demonstrates the feasibility of learning graph embeddings from brain networks, providing valuable discriminative information for diagnosing brain disorders.

Deep learning (DL) methods recently show promise on accurate brain disorder classification using functional connectivity (FC) estimated from functional magnetic resonance imaging (fMRI). However, DL model building can be hindered by small sample-size settings of fMRI. Moreover, most studies utilize either static (sFC) or dynamic FC (dFC) for classification. We propose a unified framework for data augmentation of both sFC and dFC for multi-domain joint classification of brain disorders. We exploit generative adversarial networks (GAN) to synthesize realistic FCs for data augmentation. Notably, we adopted the TimeGAN for dFC generation that can capture temporal dependencies in real dFC, and the GR-SPD-GAN for sFC generation that preserves the spatial connectivity structure. We further develop BrainFusionNet - a specialized DL model for multi-domain FC that simultaneously learns embedded features from both sFC and dFC to provide complementary spatio-temporal information for downstream classification. The synthetic FC data are augmented in training data to improve the BrainFusionNet performance and generalizability. Experimental results on major depressive disorder (MDD) identification using resting-state fMRI show substantial improvement in classification accuracy by our framework, outperforming competing models without FC augmentation and using sFC or dFC features alone.

We propose a novel algorithm to extract frequency-band specific and non-linear Granger causality (Spectral NLGC) connections between components of a multivariate time series. The advantage of our model over traditionally used VAR based models, as demonstrated in simulations, is the ability to capture complex dependence structures in a network. In addition to the simulations, the proposed method uncovered non-linear dynamics in an epileptic seizure EEG data. Spectral NLGC gives new meaningful insights into frequency specific connectivity changes at the onset of epileptic seizure. Results of both simulated and brain signals confirm the viability of the proposed algorithm as a good tool for exploration of directed connectivity in a network.

Recent applications of pattern recognition techniques to brain connectome-based classification focus on static functional connectivity (FC) neglecting the dynamics of FC over time, and use input connectivity matrices on a regular Euclidean grid. We exploit the graph convolutional networks (GCNs) to learn irregular structural patterns in brain FC networks and propose extensions to capture dynamic changes in network topology. We develop a dynamic graph autoencoder (DyGAE)-based framework to leverage the time-varying topological structures of dynamic brain networks for identification of autism spectrum disorder (ASD). The framework combines a GCN-based DyGAE to encode individual-level dynamic networks into time-varying low-dimensional network embeddings, and classifiers based on weighted fully-connected neural network (FCNN) and long short-term memory (LSTM) to facilitate dynamic graph classification via the learned spatial-temporal information. Evaluation on a large ABIDE resting-state functional magnetic resonance imaging (rs-fMRI) dataset shows that our method outperformed state-of-the-art methods in detecting altered FC in ASD. Dynamic FC analyses with DyGAE learned embeddings also reveal apparent group difference between ASD and healthy controls in network profiles and switching dynamics of brain states.

We consider the challenges in extracting stimulus-related neural dynamics from other intrinsic processes and noise in naturalistic functional magnetic resonance imaging (fMRI). Most studies rely on inter-subject correlations (ISC) of low-level regional activity and neglect varying responses in individuals. We propose a novel, data-driven approach based on low-rank plus sparse ( [Formula: see text]) decomposition to isolate stimulus-driven dynamic changes in brain functional connectivity (FC) from the background noise, by exploiting shared network structure among subjects receiving the same naturalistic stimuli. The time-resolved multi-subject FC matrices are modeled as a sum of a low-rank component of correlated FC patterns across subjects, and a sparse component of subject-specific, idiosyncratic background activities. To recover the shared low-rank subspace, we introduce a fused version of principal component pursuit (PCP) by adding a fusion-type penalty on the differences between the columns of the low-rank matrix. The method improves the detection of stimulus-induced group-level homogeneity in the FC profile while capturing inter-subject variability. We develop an efficient algorithm via a linearized alternating direction method of multipliers to solve the fused-PCP. Simulations show accurate recovery by the fused-PCP even when a large fraction of FC edges are severely corrupted. When applied to natural fMRI data, our method reveals FC changes that were time-locked to auditory processing during movie watching, with dynamic engagement of sensorimotor systems for speech-in-noise. It also provides a better mapping to auditory content in the movie than ISC.

OBJECTIVE: We present a unified statistical framework for characterizing community structure of brain functional networks that captures variation across individuals and evolution over time. Existing methods for community detection focus only on single-subject analysis of dynamic networks; while recent extensions to multiple-subjects analysis are limited to static networks. METHOD: To overcome these limitations, we propose a multi-subject, Markov-switching stochastic block model (MSS-SBM) to identify state-related changes in brain community organization over a group of individuals. We first formulate a multilayer extension of SBM to describe the time-dependent, multi-subject brain networks. We develop a novel procedure for fitting the multilayer SBM that builds on multislice modularity maximization which can uncover a common community partition of all layers (subjects) simultaneously. By augmenting with a dynamic Markov switching process, our proposed method is able to capture a set of distinct, recurring temporal states with respect to inter-community interactions over subjects and the change points between them. RESULTS: Simulation shows accurate community recovery and tracking of dynamic community regimes over multilayer networks by the MSS-SBM. Application to task fMRI reveals meaningful non-assortative brain community motifs, e.g., core-periphery structure at the group level, that are associated with language comprehension and motor functions suggesting their putative role in complex information integration. Our approach detected dynamic reconfiguration of modular connectivity elicited by varying task demands and identified unique profiles of intra and inter-community connectivity across different task conditions. CONCLUSION: The proposed multilayer network representation provides a principled way of detecting synchronous, dynamic modularity in brain networks across subjects.

OBJECTIVE: We consider challenges in accurate segmentation of heart sound signals recorded under noisy clinical environments for subsequent classification of pathological events. Existing state-of-the-art solutions to heart sound segmentation use probabilistic models such as hidden Markov models (HMMs), which, however, are limited by its observation independence assumption and rely on pre-extraction of noise-robust features. METHODS: We propose a Markov-switching autoregressive (MSAR) process to model the raw heart sound signals directly, which allows efficient segmentation of the cyclical heart sound states according to the distinct dependence structure in each state. To enhance robustness, we extend the MSAR model to a switching linear dynamic system (SLDS) that jointly model both the switching AR dynamics of underlying heart sound signals and the noise effects. We introduce a novel algorithm via fusion of switching Kalman filter and the duration-dependent Viterbi algorithm, which incorporates the duration of heart sound states to improve state decoding. RESULTS: Evaluated on Physionet/CinC Challenge 2016 dataset, the proposed MSAR-SLDS approach significantly outperforms the hidden semi-Markov model (HSMM) in heart sound segmentation based on raw signals and comparable to a feature-based HSMM. The segmented labels were then used to train Gaussian-mixture HMM classifier for identification of abnormal beats, achieving high average precision of 86.1% on the same dataset including very noisy recordings. CONCLUSION: The proposed approach shows noticeable performance in heart sound segmentation and classification on a large noisy dataset. SIGNIFICANCE: It is potentially useful in developing automated heart monitoring systems for pre-screening of heart pathologies.

OBJECTIVE: We exploit altered patterns in brain functional connectivity as features for automatic discriminative analysis of neuropsychiatric patients. Deep learning methods have been introduced to functional network classification only very recently for fMRI, and the proposed architectures essentially focused on a single type of connectivity measure. METHODS: We propose a deep convolutional neural network (CNN) framework for classification of electroencephalogram (EEG)-derived brain connectome in schizophrenia (SZ). To capture complementary aspects of disrupted connectivity in SZ, we explore combination of various connectivity features consisting of time and frequency-domain metrics of effective connectivity based on vector autoregressive model and partial directed coherence, and complex network measures of network topology. We design a novel multi-domain connectome CNN (MDC-CNN) based on a parallel ensemble of 1D and 2D CNNs to integrate the features from various domains and dimensions using different fusion strategies. We also consider an extension to dynamic brain connectivity using the recurrent neural networks. RESULTS: Hierarchical latent representations learned by the multiple convolutional layers from EEG connectivity reveals apparent group differences between SZ and healthy controls (HC). Results on a large resting-state EEG dataset show that the proposed CNNs significantly outperform traditional support vector machine classifier. The MDC-CNN with combined connectivity features further improves performance over single-domain CNNs using individual features, achieving remarkable accuracy of 91.69% with a decision-level fusion. CONCLUSION: The proposed MDC-CNN by integrating information from diverse brain connectivity descriptors is able to accurately discriminate SZ from HC. SIGNIFICANCE: The new framework is potentially useful for developing diagnostic tools for SZ and other disorders.

Detrended Fluctuation Analysis (DFA) is a statistical estimation algorithm used to assess long-range temporal dependence in neural time series. The algorithm produces a single number, the DFA exponent, that reflects the strength of long-range temporal correlations in the data. No methods have been developed to generate confidence intervals for the DFA exponent for a single time series segment. Thus, we present a statistical measure of uncertainty for the DFA exponent in electroencephalographic (EEG) data via application of a moving-block bootstrap (MBB). We tested the effect of three data characteristics on the DFA exponent: (1) time series length, (2) the presence of artifacts, and (3) the presence of discontinuities. We found that signal lengths of ∼5 minutes produced stable measurements of the DFA exponent and that the presence of artifacts positively biased DFA exponent distributions. In comparison, the impact of discontinuities was small, even those associated with artifact removal. We show that it is possible to combine a moving block bootstrap with DFA to obtain an accurate estimate of the DFA exponent as well as its associated confidence intervals in both simulated data and human EEG data. We applied the proposed method to human EEG data to (1) calculate a time-varying estimate of long-range temporal dependence during a sleep-wake cycle of a healthy infant and (2) compare pre- and post-treatment EEG data within individual subjects with pediatric epilepsy. Our proposed method enables dynamic tracking of the DFA exponent across the entire recording period and permits within-subject comparisons, expanding the utility of the DFA algorithm by providing a measure of certainty and formal tests of statistical significance for the estimation of long-range temporal dependence in neural data.

This paper proposes a framework based on deep convolutional neural networks (CNNs) for automatic heart sound classification using short-segments of individual heart beats. We design a 1D-CNN that directly learns features from raw heart-sound signals, and a 2D-CNN that takes inputs of two-dimensional time-frequency feature maps based on Mel-frequency cepstral coefficients. We further develop a time-frequency CNN ensemble (TF-ECNN) combining the 1D-CNN and 2D-CNN based on score-level fusion of the class probabilities. On the large PhysioNet CinC challenge 2016 database, the proposed CNN models outperformed traditional classifiers based on support vector machine and hidden Markov models with various hand-crafted time- and frequency-domain features. Best classification scores with 89.22% accuracy and 89.94% sensitivity were achieved by the ECNN, and 91.55% specificity and 88.82% modified accuracy by the 2D-CNN alone on the test set.

Topological data analysis (TDA) extracts hidden topological features in signals that cannot be easily decoded by standard signal processing tools. A key TDA method is persistent homology (PH), which summarizes the changes of connected components in a signal through a multiscale descriptor such as the persistent landscape (PL). A recent development indicates that statistical inference on PLs of scalp electroencephalographic (EEG) signals produces markers for localizing seizure foci. However, a key obstacle of applying PH to large-scale clinical EEGs is the ambiguity of performing statistical inference. To address this problem, we develop a unified permutation-based inference framework for testing statistical indifference in PLs of EEG signals before and during an epileptic seizure. Compared with the standard permutation test, the proposed framework is shown to have more robustness when signals undergo non-topological changes and more sensitivity when topological changes occur. Furthermore, the proposed new method drastically improves the average computation time by 15000 folds.

Dynamic functional connectivity, as measured by the time-varying covariance of neurological signals, is believed to play an important role in many aspects of cognition. While many methods have been proposed, reliably establishing the presence and characteristics of brain connectivity is challenging due to the high dimensionality and noisiness of neuroimaging data. We present a latent factor Gaussian process model which addresses these challenges by learning a parsimonious representation of connectivity dynamics. The proposed model naturally allows for inference and visualization of the time-varying connectivity. As an illustration of the scientific utility of the model, application to a data set of rat local field potential activity recorded during a complex non-spatial memory task provides evidence of stimuli differentiation.

In this study, the monofractal and multifractal properties of inter‐beat (R‐R) intervals in cardiac signals for normal and pathology classes were studied and applied to a dataset in PhysioNet which consists of 24 h R‐R intervals from 54 healthy subjects (hs) and 92 patients with various diagnoses [44 with congestive heart failure (chf), 25 with atrial fibrillation (af) and 23 diagnosed with sudden death syndrome (sd)]. The results in this study indicate that the most suitable method for estimating the monofractal properties of R‐R intervals is detrending moving average (DMA). The Hurst exponents ( H ) of the healthy and pathological groups, calculated using the DMA method, are shown to be statistically different by the Kruskal–Wallis test [ p‐value < 0.01; healthy = 0.23(0.18–0.27); pathological group = 0.06(0.03–0.10), = 0.05(0.03–0.07), = 0.05(0.03–0.08)]. To study the multifractal properties of R‐R intervals, the multifractal detrended fluctuation analysis was used. Formal statistical tests indicate statistically significant differences ( p‐value < 0.05, ANOVA and pairwise testing) between the width of the spectrum of the chf group = 1.11 ± 0.12 and the width of the spectra of the af group = 0.58 ± 0.15, the sd group = 0.60 ± 0.20, and the hs group = 0.61 ± 0.08. Using these results, a logistic regression model was developed for differentiating chf from other pathologies (af and sd).

We consider the challenges in estimating the state-related changes in brain connectivity networks with a large number of nodes. Existing studies use the sliding-window analysis or time-varying coefficient models, which are unable to capture both smooth and abrupt changes simultaneously, and rely on ad-hoc approaches to the high-dimensional estimation. To overcome these limitations, we propose a Markov-switching dynamic factor model, which allows the dynamic connectivity states in functional magnetic resonance imaging (fMRI) data to be driven by lower-dimensional latent factors. We specify a regime-switching vector autoregressive (SVAR) factor process to quantity the time-varying directed connectivity. The model enables a reliable, data-adaptive estimation of change-points of connectivity regimes and the massive dependencies associated with each regime. We develop a three-step estimation procedure: 1) extracting the factors using principal component analysis, 2) identifying connectivity regimes in a low-dimensional subspace based on the factor-based SVAR model, and 3) constructing high-dimensional state connectivity metrics based on the subspace estimates. Simulation results show that our estimator outperforms -means clustering of time-windowed coefficients, providing more accurate estimate of time-evolving connectivity. It achieves percentage of reduction in mean squared error by 60% when the network dimension is comparable to the sample size. When applied to the resting-state fMRI data, our method successfully identifies modular organization in the resting-statenetworksin consistencywith other studies. It further reveals changes in brain states with variations across subjects and distinct large-scale directed connectivity patterns across states.

We propose a scalable semiparametric Bayesian model to capture dependencies among multiple neurons by detecting their cofiring (possibly with some lag time) patterns over time. After discretizing time so there is at most one spike at each interval, the resulting sequence of 1s (spike) and 0s (silence) for each neuron is modeled using the logistic function of a continuous latent variable with a gaussian process prior. For multiple neurons, the corresponding marginal distributions are coupled to their joint probability distribution using a parametric copula model. The advantages of our approach are as follows. The nonparametric component (i.e., the gaussian process model) provides a flexible framework for modeling the underlying firing rates, and the parametric component (i.e., the copula model) allows us to make inferences regarding both contemporaneous and lagged relationships among neurons. Using the copula model, we construct multivariate probabilistic models by separating the modeling of univariate marginal distributions from the modeling of a dependence structure among variables. Our method is easy to implement using a computationally efficient sampling algorithm that can be easily extended to high-dimensional problems. Using simulated data, we show that our approach could correctly capture temporal dependencies in firing rates and identify synchronous neurons. We also apply our model to spike train data obtained from prefrontal cortical areas.