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Jose M. Peña

  1. Towards Optimal Learning of Chain Graphs.

    Tue, 09/27/2011 - 15:01 — SomNambul
    Authors: Jose M. Peña
    Subjects: Machine Learning
    Abstract

    In this paper, we extend Meek's conjecture (Meek 1997) from directed and
    acyclic graphs to chain graphs, and prove that the extended conjecture is true.
    Specifically, we prove that if a chain graph H is an independence map of the
    independence model induced by another chain graph G, then (i) G can be
    transformed into H by a sequence of directed and undirected edge additions and
    feasible splits and mergings, and (ii) after each operation in the sequence H
    remains an independence map of the independence model induced by G.

  2. Reading Dependencies from Covariance Graphs.

    Fri, 01/14/2011 - 16:01 — SomNambul
    Authors: Jose M. Peña
    Subjects: Machine Learning
    Abstract

    The covariance graph (aka bi-directed graph) of a probability distribution
    $p$ is the undirected graph $G$ where two nodes are adjacent iff their
    corresponding random variables are marginally dependent in $p$. In this paper,
    we present a graphical criterion for reading dependencies from $G$, under the
    assumption that $p$ satisfies the graphoid properties as well as weak
    transitivity and composition. We prove that the graphical criterion is sound
    and complete in certain sense. We argue that our assumptions are not too
    restrictive.

  3. A Correction of "Deriving a Minimal I-Map of a Belief Network Relative to a Target Ordering of its Nodes".

    Tue, 01/11/2011 - 16:01 — SomNambul
    Authors: Jose M. Peña
    Subjects: Machine Learning
    Abstract

    Matzkevich and Abramson (1993b) develop two algorithms, called Methods A and
    B, for efficiently deriving the minimal directed independence map of a directed
    and acyclic graph relative to a given node ordering. Methods A and B are
    claimed to be correct although no proof is provided (a proof is just sketched).
    In this paper, we show that Methods A and B are not correct and propose a
    correction of them.

  4. Faithfulness in Chain Graphs: The Gaussian Case.

    Mon, 08/16/2010 - 15:01 — SomNambul
    Authors: Jose M. Peña
    Subjects: Machine Learning
    Abstract

    This paper deals with chain graphs under the classic
    Lauritzen-Wermuth-Frydenberg interpretation. We prove that the regular Gaussian
    distributions that factorize with respect to a chain graph $G$ with $d$
    parameters have positive Lebesgue measure with respect to $\mathbb{R}^d$,
    whereas those that factorize with respect to $G$ but are not faithful to it
    have zero Lebesgue measure with respect to $\mathbb{R}^d$. This means that, in
    the measure-theoretic sense described, almost all the regular Gaussian
    distributions that factorize with respect to $G$ are faithful to it.

Math-arch

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