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2015 ; 102
(1
): 47-64
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Selection and estimation for mixed graphical models
#MMPMID27625437
Chen S
; Witten DM
; Shojaie A
Biometrika
2015[Mar]; 102
(1
): 47-64
PMID27625437
show ga
We consider the problem of estimating the parameters in a pairwise graphical
model in which the distribution of each node, conditioned on the others, may have
a different exponential family form. We identify restrictions on the parameter
space required for the existence of a well-defined joint density, and establish
the consistency of the neighbourhood selection approach for graph reconstruction
in high dimensions when the true underlying graph is sparse. Motivated by our
theoretical results, we investigate the selection of edges between nodes whose
conditional distributions take different parametric forms, and show that
efficiency can be gained if edge estimates obtained from the regressions of
particular nodes are used to reconstruct the graph. These results are illustrated
with examples of Gaussian, Bernoulli, Poisson and exponential distributions. Our
theoretical findings are corroborated by evidence from simulation studies.