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A central question in neuroscience is how self-organizing dynamic interactions in the brain emerge on their relatively static structural backbone. Due to the complexity of spatial and temporal dependencies between different brain areas,…
In conducting non-linear dimensionality reduction and feature learning, it is common to suppose that the data lie near a lower-dimensional manifold. A class of model-based approaches for such problems includes latent variables in an unknown…
Granger-Geweke causality (GGC) is a powerful and popular method for identifying directed functional (`causal') connectivity in neuroscience. In a recent paper, Stokes and Purdon [1] raise several concerns about its use. They make two…
With the introduction of the variational autoencoder (VAE), probabilistic latent variable models have received renewed attention as powerful generative models. However, their performance in terms of test likelihood and quality of generated…
There is an increasing recognition of the role of brain networks as neuroimaging biomarkers in mental health and psychiatric studies. Our focus is posttraumatic stress disorder (PTSD), where the brain network interacts with environmental…
We propose a method of analysis of dynamical networks based on a recent measure of Granger causality between time series, based on kernel methods. The generalization of kernel Granger causality to the multivariate case, here presented,…
Granger causality (GC), a popular statistical method for the inference of directional influences between time series measured from a complex network, is sensitive to high-order (non-pairwise) interactions which fundamentally shape the…
Technological advancements in noninvasive imaging facilitate the construction of whole brain interconnected networks, known as brain connectivity. Existing approaches to analyze brain connectivity frequently disaggregate the entire network…
Under a high-dimensional vector autoregressive (VAR) model, we propose a way of efficiently estimating both the stationary graph structure between the nodal time series and their temporal dynamics. The framework is then used to make…
Granger causality, commonly used for inferring causal structures from time series data, has been adopted in widespread applications across various fields due to its intuitive explainability and high compatibility with emerging deep neural…
We propose causal recurrent variational autoencoder (CR-VAE), a novel generative model that is able to learn a Granger causal graph from a multivariate time series x and incorporates the underlying causal mechanism into its data generation…
Probabilistic approaches for tensor factorization aim to extract meaningful structure from incomplete data by postulating low rank constraints. Recently, variational Bayesian (VB) inference techniques have successfully been applied to large…
The classical vector autoregressive model is a fundamental tool for multivariate time series analysis. However, it involves too many parameters when the number of time series and lag order are even moderately large. This paper proposes to…
Estimating causal relations is vital in understanding the complex interactions in multivariate time series. Non-linear coupling of variables is one of the major challenges inaccurate estimation of cause-effect relations. In this paper, we…
Advances in sensing technology have made it possible to collect large volumes of high-dimensional time-series data. In fields like genetics and neuroscience, key questions concern whether directed relationships between variables can be…
Many problems in computational neuroscience, neuroinformatics, pattern/image recognition, signal processing and machine learning generate massive amounts of multidimensional data with multiple aspects and high dimensionality. Tensors (i.e.,…
Multivariate network time series are ubiquitous in modern systems, yet existing network autoregressive models typically treat nodes as scalar processes, ignoring cross-variable spillovers. To capture these complex interactions without the…
Recently, there has been increased interest in fusing multimodal imaging to better understand brain organization. Specifically, accounting for knowledge of anatomical pathways connecting brain regions should lead to desirable outcomes such…
Modern recording techniques enable neuroscientists to simultaneously study neural activity across large populations of neurons, with capturing predictor-dependent correlations being a fundamental challenge in neuroscience. Moreover, the…
Incorporating nonlinearity is paramount to predicting the future states of a dynamical system, its response to shocks, and its underlying causal network. However, most existing methods for causality detection and impulse response, such as…