Within diagnostic reasoning there have been a number of proposed definitions of a diagnosis, and thus of the most likely diagnosis, including most probable posterior hypothesis, most probable interpretation, most probable covering hypothesis, etc. Most of these approaches assume that the most likely diagnosis must be computed, and that a definition of what should be computed can be made a priori, independent of what the diagnosis is used for. We argue that the diagnostic problem, as currently posed, is incomplete: it does not consider how the diagnosis is to be used, or the utility associated with the treatment of the abnormalities. In this paper we analyze several well-known definitions of diagnosis, showing that the different definitions of the most likely diagnosis have different qualitative meanings, even given the same input data. We argue that the most appropriate definition of (optimal) diagnosis needs to take into account the utility of outcomes and what the diagnosis is used for.
This paper discusses how conflicts (as used by the consistency-based diagnosis community) can be adapted to be used in a search-based algorithm for computing prior and posterior probabilities in discrete Bayesian Networks. This is an "anytime" algorithm, that at any stage can estimate the probabilities and give an error bound. Whereas the most popular Bayesian net algorithms exploit the structure of the network for efficiency, we exploit probability distributions for efficiency; this algorithm is most suited to the case with extreme probabilities. This paper presents a solution to the inefficiencies found in naive algorithms, and shows how the tools of the consistency-based diagnosis community (namely conflicts) can be used effectively to improve the efficiency. Empirical results with networks having tens of thousands of nodes are presented.
We evaluate current explanation schemes. These are either insufficiently general, or suffer from other serious drawbacks. We propose a domain-independent explanation system that is based on ignoring irrelevant variables in a probabilistic setting. We then prove important properties of some specific irrelevance-based schemes and discuss how to implement them.
We describe a technique for speeding up inference for model-based abduction tasks that trades off inference time and/or space for the fraction of queries correctly answered. We compile a knowledge base (for which inference may be intractable) into a set of rules that cover the most likely queries using simple criteria that do not entail extensive knowledge engineering effort, such as subset-minimal or most probable query-responses. We demonstrate this approach on the abduction task of model-based diagnosis, and show that this approach can predictably produce order-of-magnitude reductions in time and memory requirements for abductive tasks in which the queries have skewed distributions; for example, in diagnosis the faults are skewed towards being highly unlikely.
Bayesian networks are directed acyclic graphs representing independence relationships among a set of random variables. A random variable can be regarded as a set of exhaustive and mutually exclusive propositions. We argue that there are several drawbacks resulting from the propositional nature and acyclic structure of Bayesian networks. To remedy these shortcomings, we propose a probabilistic network where nodes represent unary predicates and which may contain directed cycles. The proposed representation allows us to represent domain knowledge in a single static network even though we cannot determine the instantiations of the predicates before hand. The ability to deal with cycles also enables us to handle cyclic causal tendencies and to recognize recursive plans.