Search

We present conditions under which one can bound the probabilistic relationships between random variables in a Bayesian network by exploiting known or induced qualitative relationships. Generic strengthening and weakening operations produce bounds on cumulative distributions, and the directions of these bounds are maintained through qualitative influences. We show how to incorporate these operations in a state-space abstraction method, so that bounds provably tighten as an approximate network is refined. We apply these techniques to qualitative tradeoff resolution demonstrating an ability to identify qualitative relationships among random variables without exhaustively using the probabilistic information encoded in the given network. In an application to path planning, we present an anytime algorithm with run-time computable error bounds. [Copyright &y& Elsevier]

We investigate state-space abstraction methods for computing approximate probabilities with Bayesian networks. These methods approximate Bayesian networks by aggregating the states of variables. We implement an iterative approximation procedure based on this idea, and the procedure demonstrates the desirable anytime property in experiments. Further theoretical analysis reveals special properties of the approximations, and we exploit these properties to design heuristics for improving performance profiles of the iterative procedure. [Copyright &y& Elsevier]