Related papers: Partial correlation networks of Gaussian processes
When dealing with time series data, causal inference methods often employ structural vector autoregressive (SVAR) processes to model time-evolving random systems. In this work, we rephrase recursive SVAR processes with possible latent…
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…
Causal discovery aims to infer causal relationships among variables from observational data, typically represented by a directed acyclic graph (DAG). Most existing methods assume independent and identically distributed observations, an…
High dimensional piecewise stationary graphical models represent a versatile class for modelling time varying networks arising in diverse application areas, including biology, economics, and social sciences. There has been recent work in…
Graphical causal models are an important tool for knowledge discovery because they can represent both the causal relations between variables and the multivariate probability distributions over the data. Once learned, causal graphs can be…
Nonstationary Gaussian processes (GPs) are essential for modeling complex, locally heterogeneous spatial data. A common modeling approach is the spatial deformation method that warps the domain to recover isotropy. However, this static…
This paper focuses on the analysis of spatially correlated functional data. The between-curve correlation is modeled by correlating functional principal component scores of the functional data. We propose a Spatial Principal Analysis by…
Motivated by modern data forms such as images and multi-view data, the multi-attribute graphical model aims to explore the conditional independence structure among vectors. Under the Gaussian assumption, the conditional independence between…
A fundamental challenge of scientific research is inferring causal relations based on observed data. One commonly used approach involves utilizing structural causal models that postulate noisy functional relations among interacting…
Given a causal graph representing the data-generating process shared across different domains/distributions, enforcing sufficient graph-implied conditional independencies can identify domain-general (non-spurious) feature representations.…
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…
Graphical modeling explores dependences among a collection of variables by inferring a graph that encodes pairwise conditional independences. For jointly Gaussian variables, this translates into detecting the support of the precision…
It is well known that the dependence structure for jointly Gaussian variables can be fully captured using correlations, and that the conditional dependence structure in the same way can be described using partial correlations. The partial…
Gene regulatory networks play a crucial role in controlling an organism's biological processes, which is why there is significant interest in developing computational methods that are able to extract their structure from high-throughput…
We present a new strategy for learning the functional relation between a pair of variables, while addressing inhomogeneities in the correlation structure of the available data, by modelling the sought function as a sample function of a…
The marginal correlation between two variables is a measure of their linear dependence. The two original variables need not interact directly, because marginal correlation may arise from the mediation of other variables in the system. The…
Gaussian Process (GP) models provide a flexible framework for prediction and uncertainty quantification. For most covariance functions, however, exact GP prediction with $n$ points scales as $\mathcal{O}(n^3)$, making it prohibitively…
Off-the-shelf Gaussian Process (GP) covariance functions encode smoothness assumptions on the structure of the function to be modeled. To model complex and non-differentiable functions, these smoothness assumptions are often too…
We introduce the concept of numerical Gaussian processes, which we define as Gaussian processes with covariance functions resulting from temporal discretization of time-dependent partial differential equations. Numerical Gaussian processes,…
Identifying relationships among stochastic processes is a core objective in many fields, such as economics. While the standard toolkit for multivariate time series analysis has many advantages, it can be difficult to capture nonlinear…