Probabilistic Interpretations for MYCIN's Certainty Factors (1304.3419v1)

Abstract: This paper examines the quantities used by MYCIN to reason with uncertainty, called certainty factors. It is shown that the original definition of certainty factors is inconsistent with the functions used in MYCIN to combine the quantities. This inconsistency is used to argue for a redefinition of certainty factors in terms of the intuitively appealing desiderata associated with the combining functions. It is shown that this redefinition accommodates an unlimited number of probabilistic interpretations. These interpretations are shown to be monotonic transformations of the likelihood ratio p(EIH)/p(El H). The construction of these interpretations provides insight into the assumptions implicit in the certainty factor model. In particular, it is shown that if uncertainty is to be propagated through an inference network in accordance with the desiderata, evidence must be conditionally independent given the hypothesis and its negation and the inference network must have a tree structure. It is emphasized that assumptions implicit in the model are rarely true in practical applications. Methods for relaxing the assumptions are suggested.

• The paper redefines MYCIN's certainty factors as measures of belief change rather than static probabilities.
• It develops a probabilistic mapping using transformation functions to ensure consistency with axiomatic probability principles.
• The study refines sequential and parallel combination rules, promoting robust uncertainty propagation in expert systems.

Probabilistic Interpretations for MYCIN's Certainty Factors

The paper by David Heckerman provides an in-depth analysis of the certainty factor (CF) model used in the MYCIN expert system, offering a probabilistic interpretation of these factors to address uncertainty in rule-based systems. The research endeavors to redefine certainty factors in probabilistic terms and proposes that they represent changes in belief rather than absolute beliefs. This positioning allows the model to encompass an infinite number of probabilistic interpretations, refining the propagation of CFs through inference networks.

Overview of MYCIN's Certainty Factor Model

MYCIN uses certainty factors to manage uncertainty in medical diagnostics by attaching a CF to each rule that represents the change in belief about a hypothesis given some evidence. These certainty factors range from -1 to 1, with positive values indicating increased belief and negative values indicating decreased belief. However, traditional interpretations of CFs have been deemed inadequate due to a lack of clarity and consistency with probabilistic methods.

Probabilistic Interpretation and Theoretical Insights

The paper offers a probabilistic reinterpretation of certainty factors by aligning them with changes in probability given new evidence. This is framed within the desire that CFs should reflect belief updates in light of evidence, wherein each CF represents the change in belief about a hypothesis due to the presented evidence, as opposed to absolute belief states.

The core contributions of the paper include:

• Establishing a mapping from probabilities to CFs that involves converting probabilities into an infinite space, allowing the definition of CFs based on differences between transformed prior and posterior probabilities.
• Introducing a mapping scheme involving functions $F$ and $G$ to transition probabilities into an interval related to CFs, ensuring that the CFs adhere to axiomatic properties such as associativity, commutativity, and conditional independence.
• Addressing the requirement for CFs to be conditionally independent on a hypothesis and its negation, thereby informing the necessity of precise elicitation methods for CFs from domain experts.

Sequential and Parallel Combination Functions

The research delineates the CF propagation through networks by examining both parallel and sequential propagation rules. The parallel combination is examined in probabilistic terms and shown to be close to MYCIN's original implementation, differing slightly due to the more symmetric handling of probability updates.

Sequential combination, often more complex, assumes a hypothesis can serve as evidence for another and requires that updates reflect the interactions among various hypothesis-evidence pairs. This necessitates a distinct handling compared to MYCIN's simplistic assumptions, leading the paper to recommend modifications for more sophisticated updating schemes in line with probability theory.

Implications and Future Directions

Heckerman's work sheds light on the theoretical underpinnings of CFs and suggests enhancements for rule-based systems in handling uncertainty. The findings push for more rigorous probabilistic methods for expert systems that traditionally relied on ad-hoc decision rules.

The implications for AI and expert systems are substantial, providing a framework for more robustly integrating probabilistic reasoning in systems where uncertainty is prevalent. This can potentially improve explanation facilities and user interactions in AI systems by centering updates over absolute probabilities.

Moving forward, the research invites further exploration into the application of these probabilistic interpretations across different domains within AI, particularly in systems that require decision making under uncertainty. The comparison of empirical performance of systems using refined CFs versus traditional models would provide further evidence of the utility of this theoretical model.

Conclusion

The paper redefines certainty factors in the context of MYCIN and offers a bridge to probabilistic reasoning, enhancing the cognitive and operational coherence of expert systems that have historically leveraged CFs. By aligning CFs with probabilistic interpretations, the paper provides a vital theoretical framework that can be leveraged to augment decision-making protocols within rule-based expert systems.