Positive dependence in qualitative probabilistic networks

Qualitative probabilistic networks (QPNs) combine the conditional independence assumptions of Bayesian networks with the qualitative properties of positive and negative dependence. They formalise various intuitive properties of positive dependence to allow inferences over a large network of variables. However, we will demonstrate in this paper that, due to an incorrect symmetry property, many inferences obtained in non-binary QPNs are not mathematically true. We will provide examples of such incorrect inferences and briefly discuss possible resolutions.Comment: 10 pages, 3 figure

Qualitative approaches to quantifying probabilistic networks

A probabilistic network consists of a graphical representation (a directed graph) of the important variables in a domain of application, and the relationships between them, together with a joint probability distribution over the variables. A probabilistic network allows for computing any probability of interest. The joint probability distribution factorises into conditional probability distributions such that for each variable represented in the graph a distribution is specified conditional on all possible combinations of the variable's parents in the graph. Even for a moderate sized probabilistic network, thousands of probabilities need to be specified. Often the only source of probabilistic information is the knowledge and experience of experts. People, even experts, are known not be very good at assessing probabilities, and often dislike expressing their estimates as numbers. To overcome this problem, we propose two qualitative approaches to quantifying probabilistic networks. The first approach is abstracting away from probabilities by using qualitative probabilistic networks. The second approach is to allow the use of verbal expressions of probability during elicitation. In qualitative probabilistic networks, the arcs of the directed graph are augmented with signs: `+',`-', `0', and `?', indicating the direction of shift in probability for the variable at one end of the arc, given a shift in values of the variable at the other end of the arc. For example, a positive influence of variable A on variable B indicates that higher values for B become more likely given higher values for A. Qualitative probabilistic networks allow for reasoning with probabilistic networks in a qualitative way, thereby enabling us to check the robustness of the network's structure before probabilities are assessed. In addition, the qualitative signs provide constraints on the probabilities to be elicited. Qualitative networks are, however, not very expressive and therefore easily result in uninformative answers (`?'s) during reasoning. We will suggest several refinements of the formalism of qualitative probabilistic networks that enhance their expressiveness and applicability. To make probability elicitation easier on experts, we allow them to state verbal probability expressions, such as "probable" and "impossible", as well as numbers. To this end, we have augmented a vertical probability elicitation scale with verbal expressions. These expressions, and their position on the scale, are the result of several studies we conducted. The scale, together with other ingredients such as text-fragments describing the probability to be assessed and grouping of the probabilities that should sum to 1, is used in a newly designed probability elicitation method. The method provides for the elicitation of initial rough assessments. Assessments for which the outcome of the network is very sensitive can be refined using additional experts and/or the more conventional elicitation methods. Our method has been used with two experts in oncology in the construction of a probabilistic network for oesophageal carcinoma and allows us to elicit a large number of probabilities in little time. The experts felt comfortable with the method and evaluations of the resulting network have shown that it performs quite well with the rough assessments

Explaining inference on a population of independent agents using Bayesian networks

The main goal of this research is to design, implement, and evaluate a novel explanation method, the hierarchical explanation method (HEM), for explaining Bayesian network (BN) inference when the network is modeling a population of conditionally independent agents, each of which is modeled as a subnetwork. For example, consider disease-outbreak detection in which the agents are patients who are modeled as independent, conditioned on the factors that cause disease spread. Given evidence about these patients, such as their symptoms, suppose that the BN system infers that a respiratory anthrax outbreak is highly likely. A public-health official who received such a report would generally want to know why anthrax is being given a high posterior probability. The HEM explains such inferences. The explanation approach is applicable in general to inference on BNs that model conditionally independent agents; it complements previous approaches for explaining inference on BNs that model a single agent (e.g., for explaining the diagnostic inference for a single patient using a BN that models just that patient). The hypotheses that were tested are: (1) the proposed explanation method provides information that helps a user to understand how and why the inference results have been obtained, (2) the proposed explanation method helps to improve the quality of the inferences that users draw from evidence

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