Equivalence Between Bayesian and Credal Nets on an Updating Problem
نویسندگان
چکیده
We establish an intimate connection between Bayesian and credal nets. Bayesian nets are precise graphical models, credal nets extend Bayesian nets to imprecise probability. We focus on traditional belief updating with credal nets, and on the kind of belief updating that arises with Bayesian nets when the reason for the missingness of some of the unobserved variables in the net is unknown. We show that the two updating problems are formally the same.
منابع مشابه
Imprecise Probabilistic Graphical Models: Equivalent Representations, Inference Algorithms and Applications
Credal networks are probabilistic graphical models that extend Bayesian nets to deal with imprecision in probability, and can actually be regarded as sets of Bayesian nets. Credal nets appear to be powerful means to represent and deal with many important and challenging problems in uncertain reasoning. The counterpart of having more freedom in the modeling phase is an increased inferential comp...
متن کاملBinarization Algorithms for Approximate Updating in Credal Nets
Credal networks generalize Bayesian networks relaxing numerical parameters. This considerably expands expressivity, but makes belief updating a hard task even on polytrees. Nevertheless, if all the variables are binary, polytree-shaped credal networks can be efficiently updated by the 2U algorithm. In this paper we present a binarization algorithm, that makes it possible to approximate an updat...
متن کاملGeneralized loopy 2U: A new algorithm for approximate inference in credal networks
Credal nets generalize Bayesian nets by relaxing the requirement of precision of probabilities. Credal nets are considerably more expressive than Bayesian nets, but this makes belief updating NP-hard even on polytrees. We develop a new efficient algorithm for approximate belief updating in credal nets. The algorithm is based on an important representation result we prove for general credal nets...
متن کاملDecision-theoretic specification of credal networks: A unified language for uncertain modeling with sets of Bayesian networks
Credal networks are models that extend Bayesian nets to deal with imprecision in probability, and can actually be regarded as sets of Bayesian nets. Credal nets appear to be powerful means to represent and deal with many important and challenging problems in uncertain reasoning. We give examples to show that some of these problems can only be modeled by credal nets called non-separately specifi...
متن کاملModeling Unreliable Observations in Bayesian Networks by Credal Networks
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 ...
متن کامل