Robin J. Evans

Publications (4)0 Total impact

• Article: Markovian acyclic directed mixed graphs for discrete data

  Robin J. Evans, Thomas S. Richardson
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  ABSTRACT: Acyclic directed mixed graphs (ADMGs) are graphs that contain directed ($\rightarrow$) and bidirected ($\leftrightarrow$) edges, subject to the constraint that there are no cycles of directed edges. Such graphs may be used to represent the conditional independence structure induced by a DAG model containing hidden variables on its observed margin. The Markovian model associated with an ADMG is simply the set of distributions obeying the global Markov property, given via a simple path criterion (m-separation). We first present a factorization criterion characterizing the Markovian model that generalizes the well-known recursive factorization for DAGs. For the case of finite discrete random variables, we also provide a parametrization of the model in terms of simple conditional probabilities, and characterize its variation dependence. We show that the induced models are smooth. Consequently Markovian ADMG models for discrete variables are curved exponential families of distributions.
  01/2013;
• Source

  Available from: washington.edu

  Article: Maximum likelihood fitting of acyclic directed mixed graphs to binary data

  Robin J. Evans, Thomas S. Richardson
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  ABSTRACT: Acyclic directed mixed graphs, also known as semi-Markov models represent the conditional independence structure induced on an observed margin by a DAG model with latent variables. In this paper we present the first method for fitting these models to binary data using maximum likelihood estimation.
  03/2012;
• Source

  Available from: ArXiv

  Article: Marginal log-linear parameters for graphical Markov models

  Robin J. Evans, Thomas S. Richardson
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  ABSTRACT: Marginal log-linear (MLL) models provide a flexible approach to multivariate discrete data. MLL parametrizations under linear constraints induce a wide variety of models, including models defined by conditional independences. We introduce a sub-class of MLL models which correspond to Acyclic Directed Mixed Graphs (ADMGs) under the usual global Markov property. We characterize for precisely which graphs the resulting parametrization is variation independent. The MLL approach provides the first description of ADMG models in terms of a minimal list of constraints. The parametrization is also easily adapted to sparse modelling techniques, which we illustrate using several examples of real data.
  05/2011;
• Conference Proceeding: Maximum likelihood fitting of acyclic directed mixed graphs to binary data.

  Robin J. Evans, Thomas S. Richardson
  UAI 2010, Proceedings of the Twenty-Sixth Conference on Uncertainty in Artificial Intelligence, Catalina Island, CA, USA, July 8-11, 2010; 01/2010