Statistical analysis with missing data
Statistical analysis with missing data
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Artificial Intelligence
Updating beliefs with incomplete observations
Artificial Intelligence
International Journal of Approximate Reasoning
Conservative inference rule for uncertain reasoning under incompleteness
Journal of Artificial Intelligence Research
The inferential complexity of Bayesian and credal networks
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Graphical models for imprecise probabilities
International Journal of Approximate Reasoning
Credal sets approximation by lower probabilities: application to credal networks
IPMU'10 Proceedings of the Computational intelligence for knowledge-based systems design, and 13th international conference on Information processing and management of uncertainty
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Bayesian networks are probabilistic graphical models widely employed in AI for the implementation of knowledge-based systems. Standard inference algorithms can update the beliefs about a variable of interest in the network after the observation of some other variables. This is usually achieved under the assumption that the observations could reveal the actual states of the variables in a fully reliable way. We propose a procedure for a more general modeling of the observations, which allows for updating beliefs in different situations, including various cases of unreliable, incomplete, uncertain and also missing observations. This is achieved by augmenting the original Bayesian network with a number of auxiliary variables corresponding to the observations. For a flexible modeling of the observational process, the quantification of the relations between these auxiliary variables and those of the original Bayesian network is done by credal sets , i.e., convex sets of probability mass functions. Without any lack of generality, we show how this can be done by simply estimating the bounds of likelihoods of the observations for the different values of the observed variables. Overall, the Bayesian network is transformed into a credal network , for which a standard updating problem has to be solved. Finally, a number of transformations that might simplify the updating of the resulting credal network is provided.