Binary models for marginal independence

By Mathias Drton, Thomas S. Richardson. 2007

81 citations recorded by the source corpus.

Summary. Log‐linear models are a classical tool for the analysis of contingency tables. In particular, the subclass of graphical log‐linear models provides a general framework for modelling conditional independences. However, with the exception of special structures, marginal independence hypotheses cannot be accommodated by these traditional models. Focusing on binary variables, we present a model class that provides a framework for modelling marginal independences in contingency tables. The approach that is taken is graphical and draws on analogies with multivariate Gaussian models for marginal independence. For the graphical model representation we use bidirected graphs, which are in the tradition of path diagrams. We show how the models can be parameterized in a simple fashion, and how maximum likelihood estimation can be performed by using a version of the iterated conditional fitting algorithm. Finally we consider combining these models with symmetry restrictions.

Subfields: Artificial Intelligence, Signal Processing

View Paper: https://www.semanticscholar.org/paper/6459bf63ccbde0bb9aa25ae5960eb36844b8aade

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Citations in the corpus

Mixed Cumulative Distribution Networks (2010, methodology): “raph is a special case of a ADMG without directed edges. The absence of an edge (Xi,Xj) implies that Xi and Xj are marginally independent. Hence, bi-directed models aremodels of marginal independence [5]. Just like in a DAG, conditioning on a vertex that is the endpoint of two arrowheads will make s”
Parameter and Structure Learning in Nested Markov Models (2012, methodology): “parameterization of DAGs in terms of parameters of the form p(xi = 0| pa(xi)), and the parameterization of bidirected graph models given in [3].”
Sequences of regressions and their independences (2011, methodology): “For categorical variables, covariance graph models have been studied only more recently; see Drton and Richardson (2008), Lupparelli, Marchetti and Bergsma (2009).”
Single World Intervention Graphs ( SWIGs ) : A Unification of the Counterfactual and Graphical Approaches to Causality (2013, background): “It follows from the Möbius parametrization given in (Drton and Richardson, 2008) that such a distribution is defined by a set of equations of the form: P (Vk(a † k 1) = 0,W(a † k 2) = 0) = P (Vk(a † k 1) = 0)P (W(a † k 2) = 0) (71) where W(ak 2) is a non-empty subset of {V1, V2(a † 1 ), .”
Discrete chain graph models (2009, background): “On the other hand, the Iterative Conditional Fitting algorithm of [8] can be extended to the chain graph case, as explained in [5].”
Markov properties for mixed graphs (2011, methodology): “avebeen discussed in the literature are summary graphs [30], ancestral graphs [24], acyclic directed mixed graphs [23, 28], undirected or concentration graphs [6, 19], bidirected or covariance graphs [5, 9, 15, 31], and the class of directed acyclic graphs [11, 16, 21]. In papers on summary graphs a”
Chain graph models of multivariate regression type for categorical data (2009, background): “In the special case of a single group of responses with no explanatory variables, multivariate regression chain graphs reduce to covariance graphs, that is, to undirected graphs representing marginal independencies with the basic rule that if its subgraph is disconnected, that is, composed by comple”