A major inference task in Bayesian networks is explaining why some variables are observed in their particular states using a set of target variables. Existing methods for solving this problem often generate explanations that are either too simple (underspecified) or too complex (overspecified). In this paper, we introduce a method called Most Relevant Explanation (MRE) which finds a partial instantiation of the target variables that maximizes the generalized Bayes factor (GBF) as the best explanation for the given evidence. Our study shows that GBF has several theoretical properties that enable MRE to automatically identify the most relevant target variables in forming its explanation. In particular, conditional Bayes factor (CBF), defined as the GBF of a new explanation conditioned on an existing explanation, provides a soft measure on the degree of relevance of the variables in the new explanation in explaining the evidence given the existing explanation. As a result, MRE is able to automatically prune less relevant variables from its explanation. We also show that CBF is able to capture well the explaining-away phenomenon that is often represented in Bayesian networks. Moreover, we define two dominance relations between the candidate solutions and use the relations to generalize MRE to find a set of top explanations that is both diverse and representative. Case studies on several benchmark diagnostic Bayesian networks show that MRE is often able to find explanatory hypotheses that are not only precise but also concise.
As Bayesian Networks and Influence Diagrams are being used more and more widely, the importance of an efficient explanation mechanism becomes more apparent. We focus on predictive explanations, the ones designed to explain predictions and recommendations of probabilistic systems. We analyze the issues involved in defining, computing and evaluating such explanations and present an algorithm to compute them. Introduction As knowledge-based reasoning systems begin addressing real-world problems, they are often designed to be used not by experts but by people unfamiliar with the domain. Such people are unlikely to accept system's prediction or advice without some explanation. In addition, the systems' ever increasing size makes their computations more and more difficult to follow even for their creators. This situation makes an explanation mechanism critical for making these systems useful and widely accepted. Probabilistic systems, such as Bayesian Networks (Pearl 1988) and Influence Diagrams (Howard and Matheson 1984), need such a mechanism even more than others. Human judgment under uncertainty differs considerably from the idealized rationality of probability and decision theories.
Explanation facilities are a particularly important feature of expert system frameworks. It is an area in which traditional rule-based expert system frameworks have had mixed results. While explanations about control are well handled, facilities are needed for generating better explanations concerning knowledge base content. This paper approaches the explanation problem by examining the effect an event has on a variable of interest within a symmetric Bayesian inferencing system. We argue that any effect measure operating in this context must satisfy certain properties. Such a measure is proposed. It forms the basis for an explanation facility which allows the user of the Generalized Bayesian Inferencing System to question the meaning of the knowledge base. That facility is described in detail.
You happen to know that Tim and Harry have recently had a terrible row that ended their friendship. Now someone tells you that she just saw Tim and Harry jogging together. The best explanation for this that you can think of is that they made up. You conclude that they are friends again. One morning you enter the kitchen to find a plate and cup on the table, with breadcrumbs and a pat of butter on it, and surrounded by a jar of jam, a pack of sugar, and an empty carton of milk. You conclude that one of your house-mates got up at night to make him- or herself a midnight snack and was too tired to clear the table. This, you think, best explains the scene you are facing. To be sure, it might be that someone burgled the house and took the time to have a bite while on the job, or a house-mate might have arranged the things on the table without having a midnight snack but just to make you believe that someone had a midnight snack. But these hypotheses strike you as providing much more contrived explanations of the data than the one you infer to. Walking along the beach, you see what looks like a picture of Winston Churchill in the sand. It could be that, as in the opening pages of Hilary Putnam's (1981), what you see is actually the trace of an ant crawling on the beach. The much simpler, and therefore (you think) much better, explanation is that someone intentionally drew a picture of Churchill in the sand. That, in any case, is what you come away believing. In these examples, the conclusions do not follow logically from the premises.
An automated explanation facility for Bayesian conditioning aimed at improving user acceptance of probability-based decision support systems has been developed. The domain-independent facility is based on an information processing perspective on reasoning about conditional evidence that accounts both for biased and normative inferences. Experimental results indicate that the facility is both acceptable to naive users and effective in improving understanding.