Related papers: Graphs in State-Space Models for Granger Causality…

Many large-scale applications can be elegantly represented using graph structures. Their scalability, however, is often limited by the domain knowledge required to apply them. To address this problem, we propose a novel Causal Temporal…

Many problems encountered in science and engineering can be formulated as estimating a low-rank object (e.g., matrices and tensors) from incomplete, and possibly corrupted, linear measurements. Through the lens of matrix and tensor…

In attitude theory, formal theoretical predictions come largely from the simulation of computational models. We argue that to push attitude theory further, we should employ mathematical analysis/analytic methods alongside of computational…

In geostatistics, traditional spatial models often rely on the Gaussian Process (GP) to fit stationary covariances to data. It is well known that this approach becomes computationally infeasible when dealing with large data volumes,…

Extracting the interaction rules of biological agents from movement sequences pose challenges in various domains. Granger causality is a practical framework for analyzing the interactions from observed time-series data; however, this…

Probabilistic inference in high-dimensional state-space models is computationally challenging. For many spatiotemporal systems, however, prior knowledge about the dependency structure of state variables is available. We leverage this…

Dynamical systems comprising of multiple components that can be partitioned into distinct blocks originate in many scientific areas. A pertinent example is the interactions between financial assets and selected macroeconomic indicators,…

Causal graphs (CGs) are compact representations of the knowledge of the data generating processes behind the data distributions. When a CG is available, e.g., from the domain knowledge, we can infer the conditional independence (CI)…

The key to traffic prediction is to accurately depict the temporal dynamics of traffic flow traveling in a road network, so it is important to model the spatial dependence of the road network. The essence of spatial dependence is to…

The field of hypothesis generation promises to reduce costs in neuroscience by narrowing the range of interventional studies needed to study various phenomena. Existing machine learning methods can generate scientific hypotheses from…

We develop a causal optimization method that ensures causality in numerical calculations of Green's functions in interacting electron systems. Our method removes noncausality of numerical data by finding causal functions closest to the…

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…

Gaussian graphical models represent the underlying graph structure of conditional dependence between random variables which can be determined using their partial correlation or precision matrix. In a high-dimensional setting, the precision…

Continuum mechanics simulators, numerically solving one or more partial differential equations, are essential tools in many areas of science and engineering, but their performance often limits application in practice. Recent modern machine…

Traditionally, graph neural networks have been trained using a single observed graph. However, the observed graph represents only one possible realization. In many applications, the graph may encounter uncertainties, such as having…

Graph neural networks (GNNs) are powerful tools on graph data. However, their predictions are mis-calibrated and lack interpretability, limiting their adoption in critical applications. To address this issue, we propose a new…

Bayesian methodologies prioritising accurate associations above sparsity in Gaussian graphical model (GGM) estimation remain relatively scarce in scientific literature. It is well accepted that the $\ell_2$ penalty enjoys a smaller…

Climate system teleconnections are crucial for improving climate predictability, but difficult to quantify. Standard approaches to identify teleconnections are often based on correlations between time series. Here we present a novel method…

Regularization has become a primary tool for developing reliable estimators of the covariance matrix in high-dimensional settings. To curb the curse of dimensionality, numerous methods assume that the population covariance (or inverse…

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…