PROBABILITY DISTRIBUTIONS WITH SUMMARY GRAPH STRUCTURE

By Nanny Wermuth. 2010

63 citations recorded by the source corpus.

A set of independence statements may define the independence structure of interest in a family of joint probability distributions. This structure is often captured by a graph that consists of nodes representing the random variables and of edges that couple node pairs. One important class contains regression graphs. Regression graphs are a type of so-called chain graph and describe stepwise processes, in which at each step single or joint responses are generated given the relevant explanatory variables in their past. For joint densities that result after possible marginalising or conditioning, we introduce summary graphs. These graphs reflect the independence structure implied by the generating process for the reduced set of variables and they preserve the implied independences after additional marginalising and conditioning. They can identify generating dependences that remain unchanged and alert to possibly severe distortions due to direct and indirect confounding. Operators for matrix representations of graphs are used to derive these properties of summary graphs and to translate them into special types of paths in graphs.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/1327dd9e6cd4c2ca9a460a87528c11d3a6232952

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Citations in the corpus

Structure Learning in Graphical Modeling (2016, background): “Mixed graphs provide a useful approach to address these problems without explicit modeling of latent variables (e.g., Pearl, 2009; Spirtes et al., 2000; Wermuth, 2011).”
Multivariate Statistical Analysis (2011, methodology): “Such an edge-inducing path is also association-inducing in the corresponding model, given some mild conditions on the graph and on the distributions generated over it; see Wermuth (2010).”
Global identifiability of linear structural equation models (2010, background): “Each node uij added to the vertex set corresponds to a latent variable; compare also [11, 12, 17].”
Nested Markov Properties for Acyclic Directed Mixed Graphs (2012, background): “Much previous work (Ali et al., 2009; Evans and Richardson, 2010; Richardson and Spirtes, 2002; Sadeghi and Lauritzen, 2014; Wermuth, 2011; Wermuth et al., 1994) has defined Markov models for mixed graphs via independence constraints implied by hidden variable DAGs on the observed margin.”
Algebraic problems in structural equation modeling (2016, background): “s are summarized and represented merely in terms of correlations among the error terms in structural equations. This representation of dependence induced by latent variables is discussed in detail in [33, 44, 49, 50, 71]. Example 1.2. We take up the instrumental variable model from Example 1.1. The ”
Markov properties for mixed graphs (2011, background): “Note that in [30] a graph that is maximal is called an independence graph.”