相关论文: Star graphs induce tetrad correlations: for Gaussi…

We introduce efficient MCMC algorithms for Bayesian inference for single-factor models with correlated residuals where the residuals' distribution is a Gaussian graphical model. We call this family of models single-factor graphical models.…

To construct models of large, multivariate complex systems, such as those in biology, one needs to constrain which variables are allowed to interact. This can be viewed as detecting "local" structures among the variables. In the context of…

Population structure affects the outcome of natural selection. Static population structures can be described by graphs, where individuals occupy the nodes, and interactions occur along the edges. General conditions for evolutionary success…

Dynamic spatial graph construction is a challenge in graph neural network (GNN) for time series data problems. Although some adaptive graphs are conceivable, only a 2D graph is embedded in the network to reflect the current spatial…

In this paper we explore mathematical tools that can be used to relate directed and undirected random graph models to each other. We identify probability spaces on which a directed and an undirected graph model are equivalent, and…

Distribution shifts between training and testing datasets significantly impair the model performance on graph learning. A commonly-taken causal view in graph invariant learning suggests that stable predictive features of graphs are causally…

Directed mixed graphs permit directed and bidirected edges between any two vertices. They were first considered in the path analysis developed by Sewall Wright and play an essential role in statistical modeling. We introduce a matrix…

Bidirectional causal relationships arising from mutual interactions between variables are commonly observed within biomedical, econometrical, and social science contexts. When such relationships are further complicated by unobserved…

We discuss existence and uniqueness of stationary and ergodic nonlinear autoregressive processes when exogenous regressors are incorporated in the dynamic. To this end, we consider the convergence of the backward iterations of dependent…

This paper considers the problem of learning, from samples, the dependency structure of a system of linear stochastic differential equations, when some of the variables are latent. In particular, we observe the time evolution of some…

Motivated by the need to study the molecular mechanism underlying Type 1 Diabetes (T1D) with the gene expression data collected from both the patients and healthy controls at multiple time points, we propose an innovative method for jointly…

The spectral properties of signed directed graphs, which may be naturally obtained by assigning a sign to each edge of a directed graph, have received substantially less attention than those of their undirected and/or unsigned counterparts.…

In multivariate statistics, acyclic mixed graphs with directed and bidirected edges are widely used for compact representation of dependence structures that can arise in the presence of hidden (i.e., latent or unobserved) variables. Indeed,…

Structural causal models postulate noisy functional relations among a set of interacting variables. The causal structure underlying each such model is naturally represented by a directed graph whose edges indicate for each variable which…

A temporal (directed) graph is a graph whose edges are available only at specific times during its lifetime, $\tau$. Paths are sequences of adjacent edges whose appearing times are either strictly increasing or non-strictly increasingly…

This paper presents graph theoretic conditions for the controllability and accessibility of bilinear systems over the special orthogonal group, the special linear group and the general linear group, respectively, in the presence of drift…

The magnitude of Pearson correlation between two scalar random variables can be visually judged from the two-dimensional scatter plot of an independent and identically distributed sample drawn from the joint distribution of the two…

Imaging through scattering and random media is an outstanding problem that to date has been tackled by either measuring the medium transmission matrix or exploiting linear correlations in the transmitted speckle patterns. However,…

Inferring dependence structure through undirected graphs is crucial for uncovering the major modes of multivariate interaction among high-dimensional genomic markers that are potentially associated with cancer. Traditionally, conditional…

We derive an explicit link between Gaussian Markov random fields on metric graphs and graphical models, and in particular show that a Markov random field restricted to the vertices of the graph is, under mild regularity conditions, a…