274 research outputs found
Epistemic irrelevance in credal networks : the case of imprecise Markov trees
We replace strong independence in credal networks with the weaker notion of epistemic irrelevance. Focusing on directed trees, we show how to combine local credal sets into a global model, and we use this to construct and justify an exact message-passing algorithm that computes updated beliefs for a variable in the tree. The algorithm, which is essentially linear in the number of nodes, is formulated entirely in terms of coherent lower previsions. We supply examples of the algorithm's operation, and report an application to on-line character recognition that illustrates the advantages of our model for prediction
Epistemic irrelevance in credal nets: the case of imprecise Markov trees
We focus on credal nets, which are graphical models that generalise Bayesian
nets to imprecise probability. We replace the notion of strong independence
commonly used in credal nets with the weaker notion of epistemic irrelevance,
which is arguably more suited for a behavioural theory of probability. Focusing
on directed trees, we show how to combine the given local uncertainty models in
the nodes of the graph into a global model, and we use this to construct and
justify an exact message-passing algorithm that computes updated beliefs for a
variable in the tree. The algorithm, which is linear in the number of nodes, is
formulated entirely in terms of coherent lower previsions, and is shown to
satisfy a number of rationality requirements. We supply examples of the
algorithm's operation, and report an application to on-line character
recognition that illustrates the advantages of our approach for prediction. We
comment on the perspectives, opened by the availability, for the first time, of
a truly efficient algorithm based on epistemic irrelevance.Comment: 29 pages, 5 figures, 1 tabl
Credal Valuation Networks for Machine Reasoning Under Uncertainty
Contemporary undertakings provide limitless opportunities for widespread
application of machine reasoning and artificial intelligence in situations
characterised by uncertainty, hostility and sheer volume of data. The paper
develops a valuation network as a graphical system for higher-level fusion and
reasoning under uncertainty in support of the human operators. Valuations,
which are mathematical representation of (uncertain) knowledge and collected
data, are expressed as credal sets, defined as coherent interval probabilities
in the framework of imprecise probability theory. The basic operations with
such credal sets, combination and marginalisation, are defined to satisfy the
axioms of a valuation algebra. A practical implementation of the credal
valuation network is discussed and its utility demonstrated on a small scale
example.Comment: 16 pages, 3 figure
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