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\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\big DEPARTMENTAL SEMINAR}
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\centerline{4:15 p.m., Thursday, March 4, 2004}
\centerline{Sequoia Hall Room 200}
\centerline{(Cookies at 3:45 in 1st Floor Lounge)}

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\centerline{\sl Mathias Drton}
\centerline{\sl University of Washington}
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\centerline{\bf Iterative Conditional Fitting for Gaussian Ancestral Graph Models}
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Abstract:

Ancestral graph models, introduced by Richardson and Spirtes (2002), are a
new class of graphical models that generalizes both Markov random fields
(underlying undirected graph) and Bayesian networks (underlying DAG =
directed acyclic graph). A key feature of ancestral graphs is that they can
encode all conditional independence structures which may arise from a
Bayesian network/DAG model with selection and unobserved variables.
 
In this talk, we consider Gaussian ancestral graph models and present a new
algorithm for maximum likelihood estimation. We call this new algorithm
iterative conditional fitting (ICF) since in each step of the procedure, a
conditional distribution is estimated, subject to constraints, while a
marginal distribution is held fixed. We show that in the considered
Gaussian case, ICF may be implemented by regressions on
"pseudo-variables".  The ICF algorithm is in duality to the well-known
iterative proportional fitting algorithm, in which a marginal distribution
is fitted for a fixed conditional distribution.  Finally, the ICF approach
seems promising for future development of methodology in the case of
discrete variables.
 
This is joint work with Thomas Richardson, Department of Statistics,
University of Washington.
  


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