Related papers: Error AMP Chain Graphs
We present an objective Bayes method for covariance selection in Gaussian multivariate regression models whose error term has a covariance structure which is Markov with respect to a Directed Acyclic Graph (DAG). The scope is…
Directed graphical models provide a useful framework for modeling causal or directional relationships for multivariate data. Prior work has largely focused on identifiability and search algorithms for directed acyclic graphical (DAG)…
We introduce the Markov missing graph (MMG), a novel framework that imputes missing data based on undirected graphs. MMG leverages conditional independence relationships to locally decompose the imputation model. To establish the…
Directed acyclic graphs (DAGs) are commonly used to represent causal relationships among random variables in graphical models. Applications of these models arise in the study of physical, as well as biological systems, where directed edges…
Traditionally, graph neural networks have been trained using a single observed graph. However, the observed graph represents only one possible realization. In many applications, the graph may encounter uncertainties, such as having…
We address the problem of finding a minimal separator in an Andersson-Madigan-Perlman chain graph (AMP CG), namely, finding a set Z of nodes that separates a given nonadjacent pair of nodes such that no proper subset of Z separates that…
We consider the problem of learning the underlying causal structure among a set of variables, which are assumed to follow a Bayesian network or, more specifically, a linear recursive structural equation model (SEM) with the associated…
A Markov network characterizes the conditional independence structure, or Markov property, among a set of random variables. Existing work focuses on specific families of distributions (e.g., exponential families) and/or certain structures…
The chain graph model admits both undirected and directed edges in one graph, where symmetric conditional dependencies are encoded via undirected edges and asymmetric causal relations are encoded via directed edges. Though frequently…
Learning the structure of dependence relations between variables is a pervasive issue in the statistical literature. A directed acyclic graph (DAG) can represent a set of conditional independences, but different DAGs may encode the same set…
We introduce a statistical mechanics formalism for the study of constrained graph evolution as a Markovian stochastic process, in analogy with that available for spin systems, deriving its basic properties and highlighting the role of the…
Causal graphs, such as directed acyclic graphs (DAGs) and partial ancestral graphs (PAGs), represent causal relationships among variables in a model. Methods exist for learning DAGs and PAGs from data and for converting DAGs to PAGs.…
We consider the task of estimating a high-dimensional directed acyclic graph, given observations from a linear structural equation model with arbitrary noise distribution. By exploiting properties of common random graphs, we develop a new…
We analyze the properties of degree-preserving Markov chains based on elementary edge switchings in undirected and directed graphs. We give exact yet simple formulas for the mobility of a graph (the number of possible moves) in terms of its…
Different directed acyclic graphs (DAGs) may be Markov equivalent in the sense that they entail the same conditional independence relations among the observed variables. Meek (1995) characterizes Markov equivalence classes for DAGs (with no…
We consider graphs that represent pairwise marginal independencies amongst a set of variables (for instance, the zero entries of a covariance matrix for normal data). We characterize the directed acyclic graphs (DAGs) that faithfully…
Recently developed adaptive Markov chain Monte Carlo (MCMC) methods have been applied successfully to many problems in Bayesian statistics. Grapham is a new open source implementation covering several such methods, with emphasis on…
Neural network design has utilized flexible nonlinear processes which can mimic biological systems, but has suffered from a lack of traceability in the resulting network. Graphical probabilistic models ground network design in probabilistic…
The essential graph is a distinguished member of a Markov equivalence class of AMP chain graphs. However, the directed edges in the essential graph are not necessarily strong or invariant, i.e. they may not be shared by every member of the…
The problem of learning tree-structured Gaussian graphical models from independent and identically distributed (i.i.d.) samples is considered. The influence of the tree structure and the parameters of the Gaussian distribution on the…