
Credal nets under epistemic irrelevance
We present a new approach to credal nets, which are graphical models tha...
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Extending Factor Graphs so as to Unify Directed and Undirected Graphical Models
The two most popular types of graphical model are directed models (Bayes...
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Valuation Networks and Conditional Independence
Valuation networks have been proposed as graphical representations of va...
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Separation Properties of Sets of Probability Measures
This paper analyzes independence concepts for sets of probability measur...
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An efficient algorithm for estimating state sequences in imprecise hidden Markov models
We present an efficient exact algorithm for estimating state sequences f...
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Polynomialtime Updates of Epistemic States in a Fragment of Probabilistic Epistemic Argumentation (Technical Report)
Probabilistic epistemic argumentation allows for reasoning about argumen...
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Irrelevant and independent natural extension for sets of desirable gambles
The results in this paper add useful tools to the theory of sets of desi...
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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 messagepassing 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 online 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.
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