相关论文: Nested Covariance Determinants and Restricted Trek…
A covariance graph is an undirected graph associated with a multivariate probability distribution of a given random vector where each vertex represents each of the different components of the random vector and where the absence of an edge…
The paradigm of linear structural equation modeling readily allows one to incorporate causal feedback loops in the model specification. These appear as directed cycles in the common graphical representation of the models. However, the…
Hidden variable graphical models can sometimes imply constraints on the observable distribution that are more complex than simple conditional independence relations. These observable constraints can falsify assumptions of the model that…
Consider jointly Gaussian random variables whose conditional independence structure is specified by a graphical model. If we observe realizations of the variables, we can compute the covariance matrix, and it is well known that the support…
Identification theory for causal effects in causal models associated with hidden variable directed acyclic graphs (DAGs) is well studied. However, the corresponding algorithms are underused due to the complexity of estimating the…
In this paper, we introduce a new directed graphical model from Gaussian data: the Gaussian graphical interaction model (GGIM). The development of this model comes from considering stationary Gaussian processes on graphs, and leveraging the…
In this contribution we deal with the problem of learning an undirected graph which encodes the conditional dependence relationship between variables of a complex system, given a set of observations of this system. This is a very central…
Determining potential probability distributions with a given causal graph is vital for causality studies. To bypass the difficulty in characterizing latent variables in a Bayesian network, the nested Markov model provides an elegant…
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…
This paper characterizes the values of partial regression coefficients, defined as projection coefficients onto the space spanned by explanatory variables, for random variables generated by linear structural equation models using graphical…
Gaussian concentration graph models and covariance graph models are two classes of graphical models that are useful for uncovering latent dependence structures among multivariate variables. In the Bayesian literature, graphs are often…
We consider structural equation models in which variables can be written as a function of their parents and noise terms, which are assumed to be jointly independent. Corresponding to each structural equation model, there is a directed…
The edge structure of the graph defining an undirected graphical model describes precisely the structure of dependence between the variables in the graph. In many applications, the dependence structure is unknown and it is desirable to…
Graphical models are widely used in diverse application domains to model the conditional dependencies amongst a collection of random variables. In this paper, we consider settings where the graph structure is covariate-dependent, and…
Functional Gaussian graphical models (GGM) used for analyzing multivariate functional data customarily estimate an unknown graphical model representing the conditional relationships between the functional variables. However, in many…
We introduce priors and algorithms to perform Bayesian inference in Gaussian models defined by acyclic directed mixed graphs. Such a class of graphs, composed of directed and bi-directed edges, is a representation of conditional…
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…
In a traditional Gaussian graphical model, data homogeneity is routinely assumed with no extra variables affecting the conditional independence. In modern genomic datasets, there is an abundance of auxiliary information, which often gets…
Graphical models provide a framework for exploration of multivariate dependence patterns. The connection between graph and statistical model is made by identifying the vertices of the graph with the observed variables and translating the…