We investigate some problems related to implementation of uncertainty management, in particular the handling of computational and conceptual difficulties that easily appear in complex problems. The uncertainty polytope resulting from a set of inequality judgments on probabilities and means in a problem has very high dimension, but can be represented by a projection on a low-dimensional space if the judgments are structured into a graph with low tree-width. With this representation many judgments of independence become vacuous. The uncertainty polytope is high-dimensional and thus difficult to grasp or visualize. We propose a method to sample uniformly and efficiently from the polytope, as a means to obtain various summaries not obtainable by linear programming, such as volume, center of gravity, principal axes, etc.
Keywords. Learning, uncertainty, decomposition, uncertainty polytope
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