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Gaussian graphical models are semi-algebraic subsets of the cone of positive definite covariance matrices. Submatrices with low rank correspond to generalizations of conditional independence constraints on collections of random variables.…
Building on the theory of causal discovery from observational data, we study interactions between multiple (sets of) random variables in a linear structural equation model with non-Gaussian error terms. We give a correspondence between…
Conditional independence models associated with directed acyclic graphs (DAGs) may be characterized in at least three different ways: via a factorization, the global Markov property (given by the d-separation criterion), and the local…
Gaussian graphical models are parametric statistical models for jointly normal random variables whose dependence structure is determined by a graph. In previous work, we introduced trek separation, which gives a necessary and sufficient…
We investigate the relationship between the structure of a discrete graphical model and the support of the inverse of a generalized covariance matrix. We show that for certain graph structures, the support of the inverse covariance matrix…
We develop a criterion to certify whether causal effects are identifiable in linear structural equation models with latent variables. Linear structural equation models correspond to directed graphs whose nodes represent the random variables…
Directed Gaussian graphical models are statistical models that use a directed acyclic graph (DAG) to represent the conditional independence structures between a set of jointly normal random variables. The DAG specifies the model through…
The constraints arising from DAG models with latent variables can be naturally represented by means of acyclic directed mixed graphs (ADMGs). Such graphs contain directed and bidirected arrows, and contain no directed cycles. DAGs with…
We consider graphical models based on a recursive system of linear structural equations. This implies that there is an ordering, $\sigma$, of the variables such that each observed variable $Y_v$ is a linear function of a variable specific…
DAG models with hidden variables present many difficulties that are not present when all nodes are observed. In particular, fully observed DAG models are identified and correspond to well-defined sets ofdistributions, whereas this is not…
Graphical models are commonly used to represent conditional dependence relationships between variables. There are multiple methods available for exploring them from high-dimensional data, but almost all of them rely on the assumption that…
Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…
Graph-based causal discovery methods aim to capture conditional independencies consistent with the observed data and differentiate causal relationships from indirect or induced ones. Successful construction of graphical models of data…
In Gaussian graphical models, conditional independence and partial correlations are natural inferential targets for understanding direct relationships in multivariate data. No comparable framework exists for spatial processes, where…
Hidden variables are ubiquitous in practical data analysis, and therefore modeling marginal densities and doing inference with the resulting models is an important problem in statistics, machine learning, and causal inference. Recently, a…
Linear non-Gaussian causal models postulate that each random variable is a linear function of parent variables and non-Gaussian exogenous error terms. We study identification of the linear coefficients when such models contain latent…
In this paper we study linear non-Gaussian graphical models from the perspective of algebraic statistics. These are acyclic causal models in which each variable is a linear combination of its direct causes and independent noise. The…
Gaussian graphical models are a popular tool to learn the dependence structure in the form of a graph among variables of interest. Bayesian methods have gained in popularity in the last two decades due to their ability to simultaneously…
The Trek Separation Theorem (Sullivant et al. 2010) states necessary and sufficient conditions for a linear directed acyclic graphical model to entail for all possible values of its linear coefficients that the rank of various sub-matrices…
A linear structural equation model relates random variables of interest and corresponding Gaussian noise terms via a linear equation system. Each such model can be represented by a mixed graph in which directed edges encode the linear…