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Granger causality is widely used for causal structure discovery in complex systems from multivariate time series data. Traditional Granger causality tests based on linear models often fail to detect even mild non-linear causal…
Learning causal structures from observational data is a fundamental problem facing important computational challenges when the number of variables is large. In the context of linear structural equation models (SEMs), this paper focuses on…
Large amounts of spatial, textual, and temporal data are being produced daily. This is data containing an unstructured component (text), a spatial component (geographic position), and a time component (timestamp). Therefore, there is a need…
The estimation of time-varying quantities is a fundamental component of decision making in fields such as healthcare and finance. However, the practical utility of such estimates is limited by how accurately they quantify predictive…
We present a generalized linear structural causal model, coupled with a novel data-adaptive linear regularization, to recover causal directed acyclic graphs (DAGs) from time series. By leveraging a recently developed stochastic monotone…
We present a generalized linear structural causal model, coupled with a novel data-adaptive linear regularization, to recover causal directed acyclic graphs (DAGs) from time series. By leveraging a recently developed stochastic monotone…
We discuss the Gaussian graphical model (GGM; an undirected network of partial correlation coefficients) and detail its utility as an exploratory data analysis tool. The GGM shows which variables predict one-another, allows for sparse…
Linear dimensionality reduction methods are commonly used to extract low-dimensional structure from high-dimensional data. However, popular methods disregard temporal structure, rendering them prone to extracting noise rather than…
Time series prediction has been a long-standing research topic and an essential application in many domains. Modern time series collected from sensor networks (e.g., energy consumption and traffic flow) are often large-scale and incomplete…
Real-time monitoring in modern medical research introduces functional longitudinal data, characterized by continuous-time measurements of outcomes, treatments, and confounders. This complexity leads to uncountably infinite…
Temporal causal discovery is a crucial task aimed at uncovering the causal relations within time series data. The latest temporal causal discovery methods usually train deep learning models on prediction tasks to uncover the causality…
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…
Graph models provide efficient tools to capture the underlying structure of data defined over networks. Many real-world network topologies are subject to change over time. Learning to model the dynamic interactions between entities in such…
For the challenging task of modeling multivariate time series, we propose a new class of models that use dependent Mat\'ern processes to capture the underlying structure of data, explain their interdependencies, and predict their unknown…
The Granger framework is useful for discovering causal relations in time-varying signals. However, most Granger causality (GC) methods are developed for densely sampled timeseries data. A substantially different setting, particularly common…
This paper provides a simple, yet reliable, alternative to the (Bayesian) estimation of large multivariate VARs with time variation in the conditional mean equations and/or in the covariance structure. With our new methodology, the original…
Time-series analysis is critical for a diversity of applications in science and engineering. By leveraging the strengths of modern gradient descent algorithms, the Fourier transform, multi-resolution analysis, and Bayesian spectral…
We propose a novel framework for analyzing multivariate time series (MTS) data by integrating non-negative matrix factorization (NMF) with vector autoregression (VAR). Termed NMF-VAR, this method models the coefficient matrix of NMF as a…
This paper introduces a novel approach for modelling time-varying connectivity in neuroimaging data, focusing on the slow fluctuations in synaptic efficacy that mediate neuronal dynamics. Building on the framework of Dynamic Causal…
Generative modeling offers a promising solution to data scarcity and privacy challenges in time series analysis. However, the structural complexity of time series, characterized by multi-scale temporal patterns and heterogeneous components,…