1,876 research outputs found
Searching for Bayesian Network Structures in the Space of Restricted Acyclic Partially Directed Graphs
Although many algorithms have been designed to construct Bayesian network
structures using different approaches and principles, they all employ only two
methods: those based on independence criteria, and those based on a scoring
function and a search procedure (although some methods combine the two). Within
the score+search paradigm, the dominant approach uses local search methods in
the space of directed acyclic graphs (DAGs), where the usual choices for
defining the elementary modifications (local changes) that can be applied are
arc addition, arc deletion, and arc reversal. In this paper, we propose a new
local search method that uses a different search space, and which takes account
of the concept of equivalence between network structures: restricted acyclic
partially directed graphs (RPDAGs). In this way, the number of different
configurations of the search space is reduced, thus improving efficiency.
Moreover, although the final result must necessarily be a local optimum given
the nature of the search method, the topology of the new search space, which
avoids making early decisions about the directions of the arcs, may help to
find better local optima than those obtained by searching in the DAG space.
Detailed results of the evaluation of the proposed search method on several
test problems, including the well-known Alarm Monitoring System, are also
presented
Causal Discovery with Continuous Additive Noise Models
We consider the problem of learning causal directed acyclic graphs from an
observational joint distribution. One can use these graphs to predict the
outcome of interventional experiments, from which data are often not available.
We show that if the observational distribution follows a structural equation
model with an additive noise structure, the directed acyclic graph becomes
identifiable from the distribution under mild conditions. This constitutes an
interesting alternative to traditional methods that assume faithfulness and
identify only the Markov equivalence class of the graph, thus leaving some
edges undirected. We provide practical algorithms for finitely many samples,
RESIT (Regression with Subsequent Independence Test) and two methods based on
an independence score. We prove that RESIT is correct in the population setting
and provide an empirical evaluation
Application of new probabilistic graphical models in the genetic regulatory networks studies
This paper introduces two new probabilistic graphical models for
reconstruction of genetic regulatory networks using DNA microarray data. One is
an Independence Graph (IG) model with either a forward or a backward search
algorithm and the other one is a Gaussian Network (GN) model with a novel
greedy search method. The performances of both models were evaluated on four
MAPK pathways in yeast and three simulated data sets. Generally, an IG model
provides a sparse graph but a GN model produces a dense graph where more
information about gene-gene interactions is preserved. Additionally, we found
two key limitations in the prediction of genetic regulatory networks using DNA
microarray data, the first is the sufficiency of sample size and the second is
the complexity of network structures may not be captured without additional
data at the protein level. Those limitations are present in all prediction
methods which used only DNA microarray data.Comment: 38 pages, 3 figure
Structural Intervention Distance (SID) for Evaluating Causal Graphs
Causal inference relies on the structure of a graph, often a directed acyclic
graph (DAG). Different graphs may result in different causal inference
statements and different intervention distributions. To quantify such
differences, we propose a (pre-) distance between DAGs, the structural
intervention distance (SID). The SID is based on a graphical criterion only and
quantifies the closeness between two DAGs in terms of their corresponding
causal inference statements. It is therefore well-suited for evaluating graphs
that are used for computing interventions. Instead of DAGs it is also possible
to compare CPDAGs, completed partially directed acyclic graphs that represent
Markov equivalence classes. Since it differs significantly from the popular
Structural Hamming Distance (SHD), the SID constitutes a valuable additional
measure. We discuss properties of this distance and provide an efficient
implementation with software code available on the first author's homepage (an
R package is under construction)
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