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We describe a novel method for modeling non-stationary multivariate time series, with time-varying conditional dependencies represented through dynamic networks. Our proposed approach combines traditional multi-scale modeling and network…
Modeling sequential data has become more and more important in practice. Some applications are autonomous driving, virtual sensors and weather forecasting. To model such systems so called recurrent models are used. In this article we…
We consider the problem of inferring the conditional independence graph (CIG) of a sparse, high-dimensional, stationary matrix-variate Gaussian time series. All past work on high-dimensional matrix graphical models assumes that independent…
We propose a method for inferring the conditional indepen- dence graph (CIG) of a high-dimensional discrete-time Gaus- sian vector random process from finite-length observations. Our approach does not rely on a parametric model (such as,…
Sequences of correlated binary patterns can represent many time-series data including text, movies, and biological signals. These patterns may be described by weighted combinations of a few dominant structures that underpin specific…
In multivariate time series analysis, understanding the underlying causal relationships among variables is often of interest for various applications. Directed acyclic graphs (DAGs) provide a powerful framework for representing causal…
We propose NonStGM, a general nonparametric graphical modeling framework for studying dynamic associations among the components of a nonstationary multivariate time series. It builds on the framework of Gaussian Graphical Models (GGM) and…
We propose a flexible Bayesian approach for sparse Gaussian graphical modeling of multivariate time series. We account for temporal correlation in the data by assuming that observations are characterized by an underlying and unobserved…
We present a graph-based technique for estimating sparse covariance matrices and their inverses from high-dimensional data. The method is based on learning a directed acyclic graph (DAG) and estimating parameters of a multivariate Gaussian…
Graphical network inference is used in many fields such as genomics or ecology to infer the conditional independence structure between variables, from measurements of gene expression or species abundances for instance. In many practical…
We propose an efficient optimization algorithm for selecting a subset of training data to induce sparsity for Gaussian process regression. The algorithm estimates an inducing set and the hyperparameters using a single objective, either the…
The chain graph model admits both undirected and directed edges in one graph, where symmetric conditional dependencies are encoded via undirected edges and asymmetric causal relations are encoded via directed edges. Though frequently…
Sparse Gaussian graphical models characterize sparse dependence relationships between random variables in a network. To estimate multiple related Gaussian graphical models on the same set of variables, we formulate a hierarchical model,…
Our concern is selecting the concentration matrix's nonzero coefficients for a sparse Gaussian graphical model in a high-dimensional setting. This corresponds to estimating the graph of conditional dependencies between the variables. We…
For data segmentation in high-dimensional linear regression settings, the regression parameters are often assumed to be sparse segment-wise, which enables many existing methods to estimate the parameters locally via $\ell_1$-regularised…
We present a data-driven nonintrusive model order reduction method for dynamical systems with moving boundaries. The proposed method draws on the proper orthogonal decomposition, Gaussian process regression, and moving least squares…
Causal models seek to unravel the cause-effect relationships among variables from observed data, as opposed to mere mappings among them, as traditional regression models do. This paper introduces a novel causal discovery algorithm designed…
Ordinary differential equations (ODE) have been widely used for modeling dynamical complex systems. For high-dimensional ODE models where the number of differential equations is large, it remains challenging to estimate the ODE parameters…
Directed acyclic graphs (DAGs) are commonly used to represent causal relationships among random variables in graphical models. Applications of these models arise in the study of physical, as well as biological systems, where directed edges…
Predicting links in sparse, continuously evolving networks is a central challenge in network science. Conventional heuristic methods and deep learning models, including Graph Neural Networks (GNNs), are typically designed for static graphs…