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Thomas S. Richardson

  1. Marginal log-linear parameters for graphical Markov models.

    Wed, 05/09/2012 - 15:01 — SomNambul
    Authors: Thomas S. Richardson, Robin J. Evans
    Subjects: Methodology
    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.

  2. Maximum likelihood fitting of acyclic directed mixed graphs to binary data.

    Mon, 03/19/2012 - 15:01 — SomNambul
    Authors: Thomas S. Richardson, Robin J. Evans
    Subjects: Artificial Intelligence
    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.

  3. An Efficient Algorithm for Computing Interventional Distributions in Latent Variable Causal Models.

    Mon, 02/20/2012 - 15:01 — SomNambul
    Authors: Thomas S. Richardson, Ilya Shpitser, James M. Robins
    Subjects: Learning
    Abstract

    Probabilistic inference in graphical models is the task of computing marginal
    and conditional densities of interest from a factorized representation of a
    joint probability distribution. Inference algorithms such as variable
    elimination and belief propagation take advantage of constraints embedded in
    this factorization to compute such densities efficiently. In this paper, we
    propose an algorithm which computes interventional distributions in latent
    variable causal models represented by acyclic directed mixed graphs(ADMGs).

  4. Learning high-dimensional DAGs with latent and selection variables.

    Mon, 05/02/2011 - 15:01 — SomNambul
    Authors: Thomas S. Richardson, Marloes H. Maathuis, Markus Kalisch, Diego Colombo
    Subjects: Methodology
    Abstract

    We consider the problem of learning causal information between random
    variables in DAGs when allowing arbitrarily many latent and selection
    variables. The FCI algorithm (Spirtes et al., 1999) has been explicitly
    designed to infer conditional independence and causal information in such
    settings. However, FCI is computationally infeasible for large graphs. We
    therefore propose a new algorithm, the RFCI algorithm, which is much faster
    than FCI. In some situations the output of RFCI is slightly less informative,
    in particular with respect to conditional independence information.

  5. Markov equivalence for ancestral graphs.

    Wed, 08/26/2009 - 14:58 — SomNambul
    Authors: R. Ayesha Ali, Thomas S. Richardson, Peter Spirtes
    Subjects: gr. Statistics
    Abstract

    Ancestral graphs can encode conditional independence relations that arise in
    directed acyclic graph (DAG) models with latent and selection variables.
    However, for any ancestral graph, there may be several other graphs to which it
    is Markov equivalent. We state and prove conditions under which two maximal
    ancestral graphs are Markov equivalent to each other, thereby extending
    analogous results for DAGs given by other authors. These conditions lead to an
    algorithm for determining Markov equivalence that runs in time that is
    polynomial in the number of vertices in the graph.

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