8,502 research outputs found
Exploiting Contextual Independence In Probabilistic Inference
Bayesian belief networks have grown to prominence because they provide
compact representations for many problems for which probabilistic inference is
appropriate, and there are algorithms to exploit this compactness. The next
step is to allow compact representations of the conditional probabilities of a
variable given its parents. In this paper we present such a representation that
exploits contextual independence in terms of parent contexts; which variables
act as parents may depend on the value of other variables. The internal
representation is in terms of contextual factors (confactors) that is simply a
pair of a context and a table. The algorithm, contextual variable elimination,
is based on the standard variable elimination algorithm that eliminates the
non-query variables in turn, but when eliminating a variable, the tables that
need to be multiplied can depend on the context. This algorithm reduces to
standard variable elimination when there is no contextual independence
structure to exploit. We show how this can be much more efficient than variable
elimination when there is structure to exploit. We explain why this new method
can exploit more structure than previous methods for structured belief network
inference and an analogous algorithm that uses trees
Advances in Learning Bayesian Networks of Bounded Treewidth
This work presents novel algorithms for learning Bayesian network structures
with bounded treewidth. Both exact and approximate methods are developed. The
exact method combines mixed-integer linear programming formulations for
structure learning and treewidth computation. The approximate method consists
in uniformly sampling -trees (maximal graphs of treewidth ), and
subsequently selecting, exactly or approximately, the best structure whose
moral graph is a subgraph of that -tree. Some properties of these methods
are discussed and proven. The approaches are empirically compared to each other
and to a state-of-the-art method for learning bounded treewidth structures on a
collection of public data sets with up to 100 variables. The experiments show
that our exact algorithm outperforms the state of the art, and that the
approximate approach is fairly accurate.Comment: 23 pages, 2 figures, 3 table
Exact Inference Techniques for the Analysis of Bayesian Attack Graphs
Attack graphs are a powerful tool for security risk assessment by analysing
network vulnerabilities and the paths attackers can use to compromise network
resources. The uncertainty about the attacker's behaviour makes Bayesian
networks suitable to model attack graphs to perform static and dynamic
analysis. Previous approaches have focused on the formalization of attack
graphs into a Bayesian model rather than proposing mechanisms for their
analysis. In this paper we propose to use efficient algorithms to make exact
inference in Bayesian attack graphs, enabling the static and dynamic network
risk assessments. To support the validity of our approach we have performed an
extensive experimental evaluation on synthetic Bayesian attack graphs with
different topologies, showing the computational advantages in terms of time and
memory use of the proposed techniques when compared to existing approaches.Comment: 14 pages, 15 figure
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