91 research outputs found
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
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
Reintroducing credal networks under epistemic irrelevance
A credal network under epistemic irrelevance is a generalised version of a Bayesian network that loosens its two main building blocks. On the one hand, the local probabilities do not have to be specified exactly. On the other hand, the assumptions of independence do not have to hold exactly. Conceptually, these credal networks are elegant and useful. However, in practice, they have long remained very hard to work with, both theoretically and computationally. This paper provides a general introduction to this type of credal networks and presents some promising new theoretical developments that were recently proved using sets of desirable gambles and lower previsions. We explain these developments in terms of probabilities and expectations, thereby making them more easily accessible to the Bayesian network community
Efficient Computation of Counterfactual Bounds
We assume to be given structural equations over discrete variables inducing a
directed acyclic graph, namely, a structural causal model, together with data
about its internal nodes. The question we want to answer is how we can compute
bounds for partially identifiable counterfactual queries from such an input. We
start by giving a map from structural casual models to credal networks. This
allows us to compute exact counterfactual bounds via algorithms for credal nets
on a subclass of structural causal models. Exact computation is going to be
inefficient in general given that, as we show, causal inference is NP-hard even
on polytrees. We target then approximate bounds via a causal EM scheme. We
evaluate their accuracy by providing credible intervals on the quality of the
approximation; we show through a synthetic benchmark that the EM scheme
delivers accurate results in a fair number of runs. In the course of the
discussion, we also point out what seems to be a neglected limitation to the
trending idea that counterfactual bounds can be computed without knowledge of
the structural equations. We also present a real case study on palliative care
to show how our algorithms can readily be used for practical purposes
Generalized belief change with imprecise probabilities and graphical models
We provide a theoretical investigation of probabilistic belief revision in complex frameworks, under extended conditions of uncertainty, inconsistency and imprecision. We motivate our kinematical approach by specializing our discussion to probabilistic reasoning with graphical models, whose modular representation allows for efficient inference. Most results in this direction are derived from the relevant work of Chan and Darwiche (2005), that first proved the inter-reducibility of virtual and probabilistic evidence. Such forms of information, deeply distinct in their meaning, are extended to the conditional and imprecise frameworks, allowing further generalizations, e.g. to experts' qualitative assessments. Belief aggregation and iterated revision of a rational agent's belief are also explored
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