320 research outputs found
Credal Networks under Epistemic Irrelevance
A credal network under epistemic irrelevance is a generalised type of
Bayesian network that relaxes its two main building blocks. On the one hand,
the local probabilities are allowed to be partially specified. On the other
hand, the assessments of independence do not have to hold exactly.
Conceptually, these two features turn credal networks under epistemic
irrelevance into a powerful alternative to Bayesian networks, offering a more
flexible approach to graph-based multivariate uncertainty modelling. However,
in practice, they have long been perceived as very hard to work with, both
theoretically and computationally.
The aim of this paper is to demonstrate that this perception is no longer
justified. We provide a general introduction to credal networks under epistemic
irrelevance, give an overview of the state of the art, and present several new
theoretical results. Most importantly, we explain how these results can be
combined to allow for the design of recursive inference methods. We provide
numerous concrete examples of how this can be achieved, and use these to
demonstrate that computing with credal networks under epistemic irrelevance is
most definitely feasible, and in some cases even highly efficient. We also
discuss several philosophical aspects, including the lack of symmetry, how to
deal with probability zero, the interpretation of lower expectations, the
axiomatic status of graphoid properties, and the difference between updating
and conditioning
Inference in credal networks: branch-and-bound methods and the A/R+ algorithm
AbstractA credal network is a graphical representation for a set of joint probability distributions. In this paper we discuss algorithms for exact and approximate inferences in credal networks. We propose a branch-and-bound framework for inference, and focus on inferences for polytree-shaped networks. We also propose a new algorithm, A/R+, for outer approximations in polytree-shaped credal networks
Reliable Uncertain Evidence Modeling in Bayesian Networks by Credal Networks
A reliable modeling of uncertain evidence in Bayesian networks based on a
set-valued quantification is proposed. Both soft and virtual evidences are
considered. We show that evidence propagation in this setup can be reduced to
standard updating in an augmented credal network, equivalent to a set of
consistent Bayesian networks. A characterization of the computational
complexity for this task is derived together with an efficient exact procedure
for a subclass of instances. In the case of multiple uncertain evidences over
the same variable, the proposed procedure can provide a set-valued version of
the geometric approach to opinion pooling.Comment: 19 page
Recent advances in imprecise-probabilistic graphical models
We summarise and provide pointers to recent advances in inference and identification for specific types of probabilistic graphical models using imprecise probabilities. Robust inferences can be made in so-called credal networks when the local models attached to their nodes are imprecisely specified as conditional lower previsions, by using exact algorithms whose complexity is comparable to that for the precise-probabilistic counterparts
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