TY - JOUR

T1 - Objective Bayesian search of Gaussian directed acyclic graphical models for ordered variables with non-local priors

AU - Consonni, Guido

AU - Altomare, Davide

AU - La Rocca, Luca

PY - 2013

Y1 - 2013

N2 - Directed acyclic graphical (DAG) models are increasingly employed in the study of physical and biological systems
to model direct influences between variables. Identifying the graph from data is a challenging endeavor, which can be more
reasonably tackled if the variables are assumed to satisfy a given ordering; in this case we simply have to estimate the presence
or absence of each potential edge. Working under this assumption, we propose an objective Bayesian method for searching the
space of Gaussian DAG models, which provides a rich output from minimal input.We base our analysis on non-local parameter
priors, which are especially suited for learning sparse graphs, because they allow a faster learning rate, relative to ordinary
local parameter priors, when the true unknown sampling distribution belongs to a simple model. We implement an efficient
stochastic search algorithm, which deals effectively with data sets having sample size smaller than the number of variables,
and apply our method to a variety of simulated and real data sets. Our approach compares favorably, in terms of the ROC
curve for edge hit rate versus false alarm rate, to current state-of-the-art frequentist methods relying on the assumption of
ordered variables; under this assumption it exhibits a competitive advantage over the PC-algorithm, which can be considered
as a frequentist benchmark for unordered variables. Importantly, we find that our method is still at an advantage for learning
the skeleton of the DAG, when the ordering of the variables is only moderately mis-specified. Prospectively, our method could
be coupled with a strategy to learn the order of the variables, thus dropping the known ordering assumption.

AB - Directed acyclic graphical (DAG) models are increasingly employed in the study of physical and biological systems
to model direct influences between variables. Identifying the graph from data is a challenging endeavor, which can be more
reasonably tackled if the variables are assumed to satisfy a given ordering; in this case we simply have to estimate the presence
or absence of each potential edge. Working under this assumption, we propose an objective Bayesian method for searching the
space of Gaussian DAG models, which provides a rich output from minimal input.We base our analysis on non-local parameter
priors, which are especially suited for learning sparse graphs, because they allow a faster learning rate, relative to ordinary
local parameter priors, when the true unknown sampling distribution belongs to a simple model. We implement an efficient
stochastic search algorithm, which deals effectively with data sets having sample size smaller than the number of variables,
and apply our method to a variety of simulated and real data sets. Our approach compares favorably, in terms of the ROC
curve for edge hit rate versus false alarm rate, to current state-of-the-art frequentist methods relying on the assumption of
ordered variables; under this assumption it exhibits a competitive advantage over the PC-algorithm, which can be considered
as a frequentist benchmark for unordered variables. Importantly, we find that our method is still at an advantage for learning
the skeleton of the DAG, when the ordering of the variables is only moderately mis-specified. Prospectively, our method could
be coupled with a strategy to learn the order of the variables, thus dropping the known ordering assumption.

KW - Directed acyclic graph

KW - Fractional Bayes factor

KW - Structural learning

KW - Directed acyclic graph

KW - Fractional Bayes factor

KW - Structural learning

UR - http://hdl.handle.net/10807/43125

UR - http://onlinelibrary.wiley.com/journal/10.1111/(issn)1541-0420/earlyview

U2 - 10.1111/biom.12018

DO - 10.1111/biom.12018

M3 - Article

VL - 69

SP - 478

EP - 487

JO - Biometrics

JF - Biometrics

SN - 0006-341X

ER -