We discuss two problems: the representation of sets of probability distributions for Bayesian networks, and the issue of representing and abstracting actions using Bayesian networks. For the first problem, we propose the use of cc-trees to represent sets of probability distributions and show how propagation in Bayesian networks can be performed without loss of information in this representation. The cc-tree representation provides an intuitive and flexible way to make tradeoffs between precision and computational cost. For the second problem, we identify a class of planning problems where a simple abstraction technique can be used to abstract a set of actions and to reduce the cost of plan evaluation. Introduction Decision-theoretic approaches to planning, while representationally appealing, tend to be extremely computationally costly.
When eliciting probability models from experts, knowledge engineers may compare the results of the model with expert judgment on test scenarios, then adjust model parameters to bring the behavior of the model more in line with the expert's intuition. This paper presents a methodology for analytic computation of sensitivity values to measure the impact of small changes in a network parameter on a target probability value or distribution. These values can be used to guide knowledge elicitation. They can also be used in a gradient descent algorithm to estimate parameter values that maximize a measure of goodness-of-fit to both local and holistic probability assessments.
Lower and upper probabilities, also known as Choquet capacities, are widely used as a convenient representation for sets of probability distributions. This paper presents a graphical decomposition and exact propagation algorithm for computing marginal posteriors of 2-monotone lower probabilities (equivalently, 2-alternating upper probabilities).
This paper investigates a representation language with flexibility inspired by probabilistic logic and compactness inspired by relational Bayesian networks. The goal is to handle propositional and first-order constructs together with precise, imprecise, indeterminate and qualitative probabilistic assessments. The paper shows how this can be achieved through the theory of credal networks. New exact and approximate inference algorithms based on multilinear programming and iterated/loopy propagation of interval probabilities are presented; their superior performance, compared to existing ones, is shown empirically.