Probabilistic reasoning in decision support systems: from computation to common sense

Most areas of engineering, science, and management use important tools based on probabilistic methods. The common thread of the entire spectrum of these tools is aiding in decision making under uncertainty: the choice of an interpretation of reality or the choice of a course of action. Although the importance of dealing with uncertainty in decision making is widely acknowledged, dissemination of probabilistic and decision-theoretic methods in Artificial Intelligence has been surprisingly slow. Opponents of probability theory have pointed out three major obstacles to applying it in computerized decision aids: (1) the counterintuitiveness of probabilistic inference, which makes it hard for system builders, experts, and users to translate knowledge into probabilistic form, create knowledge bases, and to interpret results; (2) the quantitative character of probability theory, which implies collection or assessment of vast quantities of numbers and, since these are not always readily available, raises questions about their quality; and (3) closely related to its quantitative character, the computational complexity of probabilistic inference. Its proponents, on the other hand, point out that probability theory is the soundest formalism for dealing with uncertainty, outperforming its competitors in most applications. These two extreme views suggest a dilemma: is it necessary to choose between sound and intuitive inference methods? This thesis argues for choosing sound inference methods and shows that this dilemma might not be as hard as it seems. It argues that probability calculus rests on intuitive and computationally tractable foundations, which provide a good basis for building human interfaces to decision support systems. The character of this thesis is theoretical: starting from a few robust empirical premises, such as the largely qualitative character of human reasoning and the importance of causality, it develops formal methods for building human interfaces to decision support systems. With respect to the building of probabilistic models, the thesis argues on theoretical and empirical grounds, that it is essential to understand and explore the interaction between probability and causality. Rather than shying away from the human tendency to refer to causal relations in the process or knowledge elicitation, or explanation of results, one can give causality a sound meaning. This is, further, an essential step for creating intelligent planners, i.e., computer programs capable of constructing and solving decision models without human assistance. The thesis specifies formal conditions under which the structure of a Bayesian belief network can be given a causal interpretation. It demonstrates that the notion of causality in the recently proposed methods for construction of causal graphs from observations [131, 172] is almost identical with the notion of causality in econometric models [164]. Causal discovery procedures can actually be viewed as procedures for discovery of structural equations forming a model of the observed system and this view seems to offer several advantages. With respect to explaining the inference in probabilistic models, two complementary views of probabilistic reasoning are proposed: belief propagation and scenario-based reasoning. Belief propagation is based on the concept of updating the belief in a variable by determining how other variables influence it. Changes in beliefs are caused by observing how new evidence propagates through all variables that directly or indirectly depend on that evidence. Scenario-based reasoning is based on weighting the likelihoods of deterministic scenarios representing possible states of the world. The thesis takes the position that sound principles of qualitative inference should be derived from normative laws. It demonstrates the qualitative foundations of probabilistic inference in the context of Qualitative Probabilistic Networks, a formalism resting on a cognitively robust, qualitative specification of a probabilistic domain [196]. The thesis proposes an algorithm for qualitative belief propagation, a qualitative belief updating scheme with negligible computational cost. The advantage of qualitative belief propagation over the earlier, graph reduction-based algorithm is that it does not modify the network. This facilitates generation of explanations and metalevel reasoning, i.e., reasoning not only about the decision, but also about the model. The thesis describes also new insights related to intercausal reasoning [77, 198], an important element of qualitative belief propagation, and a valuable building block for any uncertain reasoning scheme on its own. The feasibility of automatic generation of explanations of probabilistic inference is demonstrated by developing the foundations for two methods of explaining probabilistic inference, one based on belief propagation and the other on scenario-based reasoning. A scenario-based algorithm for decision-theoretic inference is proposed. The algorithm converges on the optimal decision option by pruning options that are provably inferior and is particularly efficient for problems, with a clearly dominant option. Difficulties with applying scenario-based reasoning to explanation of decision-theoretic inference are discussed. It is proposed that an explanation program should be able to represent utility on a rough absolute scale with a zero point corresponding to the outcome perceived as status quo. The scenario view of decision-theoretic inference provides a useful insight into logic-based Artificial Intelligence schemes for reasoning under uncertainty. The foundations of non-monotonic logics, cost-based abduction, and model-based diagnosis are discussed. It is demonstrated that these formalisms make implicit assumptions about utility and provide meaningful results only when these assumptions are valid. In their current form, they are, therefore, not well equipped to support decision making under uncertainty in general.