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We study submodels of Gaussian DAG models defined by partial homogeneity constraints imposed on the model error variances and structural coefficients. We represent these models with colored DAGs and investigate their properties for use in…
We propose a new class of models specifically tailored for spatio-temporal data analysis. To this end, we generalize the spatial autoregressive model with autoregressive and heteroskedastic disturbances, i.e. SARAR(1,1), by exploiting the…
Building comprehensive brain connectomes has proved of fundamental importance in resting-state fMRI (rs-fMRI) analysis. Based on the foundation of brain network, spatial-temporal-based graph convolutional networks have dramatically improved…
Causal discovery, the learning of causality in a data mining scenario, has been of strong scientific and theoretical interest as a starting point to identify "what causes what?" Contingent on assumptions and a proper learning algorithm, it…
Epidemiological investigations of regionally aggregated spatial data often involve detecting spatial health disparities among neighboring regions on a map of disease mortality or incidence rates. Analyzing such data introduces spatial…
Covariate adjustment is a widely used approach to estimate total causal effects from observational data. Several graphical criteria have been developed in recent years to identify valid covariates for adjustment from graphical causal…
The literature on Gaussian graphical models (GGMs) contains two equally rich and equally significant domains of research efforts and interests. The first research domain relates to the problem of graph determination. That is, the underlying…
Discovering causal structures from multivariate time series is a key problem because interactions span across multiple lags and possibly involve instantaneous dependencies. Additionally, the search space of the dynamic graphs is…
In complex multivariate systems, interactions among variables are defined by dependency structures, often encoded as directed acyclic graphs ($\text{DAGs}$). However, dependency structures can vary across subjects, and ignoring this…
Directed acyclic graph (DAG) has been widely employed to represent directional relationships among a set of collected nodes. Yet, the available data in one single study is often limited for accurate DAG reconstruction, whereas heterogeneous…
Spatial correlation in areal unit count data is typically modelled by a set of random effects that are assigned a conditional autoregressive (CAR) prior distribution. The spatial correlation structure implied by this model depends on a…
The objective of disease mapping is to model data aggregated at the areal level. In some contexts, however, (e.g. residential histories, general practitioner catchment areas) when data is arising from a variety of sources, not necessarily…
Spatial transcriptomics technologies enable the measurement of gene expression with spatial context, providing opportunities to understand how gene regulatory networks vary across tissue regions. However, existing graphical models focus…
Observational studies in fields such as epidemiology often rely on covariate adjustment to estimate causal effects. Classical graphical criteria, like the back-door criterion and the generalized adjustment criterion, are powerful tools for…
In many application areas---lending, education, and online recommenders, for example---fairness and equity concerns emerge when a machine learning system interacts with a dynamically changing environment to produce both immediate and…
This paper studies the problem of learning the correlation structure of a set of intervention functions defined on the directed acyclic graph (DAG) of a causal model. This is useful when we are interested in jointly learning the causal…
We present a graphical approach to deriving inequality constraints for directed acyclic graph (DAG) models, where some variables are unobserved. In particular we show that the observed distribution of a discrete model is always restricted…
Graphical models based on Directed Acyclic Graphs (DAGs) are widely used to answer causal questions across a variety of scientific and social disciplines. However, observational data alone cannot distinguish in general between DAGs…
We consider distributions arising from a mixture of causal models, where each model is represented by a directed acyclic graph (DAG). We provide a graphical representation of such mixture distributions and prove that this representation…
We consider the problem of inferring the causal structure from observational data, especially when the structure is sparse. This type of problem is usually formulated as an inference of a directed acyclic graph (DAG) model. The linear…