On reasoning in networks with qualitative uncertainty

In this paper some initial work towards a new approach to qualitative reasoning under uncertainty is presented. This method is not only applicable to qualitative probabilistic reasoning, as is the case with other methods, but also allows the qualitative propagation within networks of values based upon possibility theory and Dempster-Shafer evidence theory. The method is applied to two simple networks from which a large class of directed graphs may be constructed. The results of this analysis are used to compare the qualitative behaviour of the three major quantitative uncertainty handling formalisms, and to demonstrate that the qualitative integration of the formalisms is possible under certain assumptions.Comment: Appears in Proceedings of the Ninth Conference on Uncertainty in Artificial Intelligence (UAI1993

Compiling Possibilistic Networks: Alternative Approaches to Possibilistic Inference

Qualitative possibilistic networks, also known as min-based possibilistic networks, are important tools for handling uncertain information in the possibility theory frame- work. Despite their importance, only the junction tree adaptation has been proposed for exact reasoning with such networks. This paper explores alternative algorithms using compilation techniques. We first propose possibilistic adaptations of standard compilation-based probabilistic methods. Then, we develop a new, purely possibilistic, method based on the transformation of the initial network into a possibilistic base. A comparative study shows that this latter performs better than the possibilistic adap- tations of probabilistic methods. This result is also confirmed by experimental results.Comment: Appears in Proceedings of the Twenty-Sixth Conference on Uncertainty in Artificial Intelligence (UAI2010

Pivotal Pruning of Trade-offs in QPNs

Qualitative probabilistic networks have been designed for probabilistic reasoning in a qualitative way. Due to their coarse level of representation detail, qualitative probabilistic networks do not provide for resolving trade-offs and typically yield ambiguous results upon inference. We present an algorithm for computing more insightful results for unresolved trade-offs. The algorithm builds upon the idea of using pivots to zoom in on the trade-offs and identifying the information that would serve to resolve them.Comment: Appears in Proceedings of the Sixteenth Conference on Uncertainty in Artificial Intelligence (UAI2000

Refining Reasoning in Qualitative Probabilistic Networks

In recent years there has been a spate of papers describing systems for probabilisitic reasoning which do not use numerical probabilities. In some cases the simple set of values used by these systems make it impossible to predict how a probability will change or which hypothesis is most likely given certain evidence. This paper concentrates on such situations, and suggests a number of ways in which they may be resolved by refining the representation.Comment: Appears in Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (UAI1995

Elicitation of Probabilities for Belief Networks: Combining Qualitative and Quantitative Information

Although the usefulness of belief networks for reasoning under uncertainty is widely accepted, obtaining numerical probabilities that they require is still perceived a major obstacle. Often not enough statistical data is available to allow for reliable probability estimation. Available information may not be directly amenable for encoding in the network. Finally, domain experts may be reluctant to provide numerical probabilities. In this paper, we propose a method for elicitation of probabilities from a domain expert that is non-invasive and accommodates whatever probabilistic information the expert is willing to state. We express all available information, whether qualitative or quantitative in nature, in a canonical form consisting of (in) equalities expressing constraints on the hyperspace of possible joint probability distributions. We then use this canonical form to derive second-order probability distributions over the desired probabilities.Comment: Appears in Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (UAI1995

Incremental Tradeoff Resolution in Qualitative Probabilistic Networks

Qualitative probabilistic reasoning in a Bayesian network often reveals tradeoffs: relationships that are ambiguous due to competing qualitative influences. We present two techniques that combine qualitative and numeric probabilistic reasoning to resolve such tradeoffs, inferring the qualitative relationship between nodes in a Bayesian network. The first approach incrementally marginalizes nodes that contribute to the ambiguous qualitative relationships. The second approach evaluates approximate Bayesian networks for bounds of probability distributions, and uses these bounds to determinate qualitative relationships in question. This approach is also incremental in that the algorithm refines the state spaces of random variables for tighter bounds until the qualitative relationships are resolved. Both approaches provide systematic methods for tradeoff resolution at potentially lower computational cost than application of purely numeric methods.Comment: Appears in Proceedings of the Fourteenth Conference on Uncertainty in Artificial Intelligence (UAI1998

From Qualitative to Quantitative Probabilistic Networks

Quantification is well known to be a major obstacle in the construction of a probabilistic network, especially when relying on human experts for this purpose. The construction of a qualitative probabilistic network has been proposed as an initial step in a network s quantification, since the qualitative network can be used TO gain preliminary insight IN the projected networks reasoning behaviour. We extend on this idea and present a new type of network in which both signs and numbers are specified; we further present an associated algorithm for probabilistic inference. Building upon these semi-qualitative networks, a probabilistic network can be quantified and studied in a stepwise manner. As a result, modelling inadequacies can be detected and amended at an early stage in the quantification process.Comment: Appears in Proceedings of the Eighteenth Conference on Uncertainty in Artificial Intelligence (UAI2002

A Structured, Probabilistic Representation of Action

When agents devise plans for execution in the real world, they face two important forms of uncertainty: they can never have complete knowledge about the state of the world, and they do not have complete control, as the effects of their actions are uncertain. While most classical planning methods avoid explicit uncertainty reasoning, we believe that uncertainty should be explicitly represented and reasoned about. We develop a probabilistic representation for states and actions, based on belief networks. We define conditional belief nets (CBNs) to capture the probabilistic dependency of the effects of an action upon the state of the world. We also use a CBN to represent the intrinsic relationships among entities in the environment, which persist from state to state. We present a simple projection algorithm to construct the belief network of the state succeeding an action, using the environment CBN model to infer indirect effects. We discuss how the qualitative aspects of belief networks and CBNs make them appropriate for the various stages of the problem solving process, from model construction to the design of planning algorithms.Comment: Appears in Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence (UAI1994

On the Relation between Kappa Calculus and Probabilistic Reasoning

We study the connection between kappa calculus and probabilistic reasoning in diagnosis applications. Specifically, we abstract a probabilistic belief network for diagnosing faults into a kappa network and compare the ordering of faults computed using both methods. We show that, at least for the example examined, the ordering of faults coincide as long as all the causal relations in the original probabilistic network are taken into account. We also provide a formal analysis of some network structures where the two methods will differ. Both kappa rankings and infinitesimal probabilities have been used extensively to study default reasoning and belief revision. But little has been done on utilizing their connection as outlined above. This is partly because the relation between kappa and probability calculi assumes that probabilities are arbitrarily close to one (or zero). The experiments in this paper investigate this relation when this assumption is not satisfied. The reported results have important implications on the use of kappa rankings to enhance the knowledge engineering of uncertainty models.Comment: Appears in Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence (UAI1994

Intercausal Reasoning with Uninstantiated Ancestor Nodes

Intercausal reasoning is a common inference pattern involving probabilistic dependence of causes of an observed common effect. The sign of this dependence is captured by a qualitative property called product synergy. The current definition of product synergy is insufficient for intercausal reasoning where there are additional uninstantiated causes of the common effect. We propose a new definition of product synergy and prove its adequacy for intercausal reasoning with direct and indirect evidence for the common effect. The new definition is based on a new property matrix half positive semi-definiteness, a weakened form of matrix positive semi-definiteness.Comment: Appears in Proceedings of the Ninth Conference on Uncertainty in Artificial Intelligence (UAI1993