The Automatic Training of Rule Bases that Use Numerical Uncertainty Representations

The use of numerical uncertainty representations allows better modeling of some aspects of human evidential reasoning. It also makes knowledge acquisition and sys­ tem development, test, and modification more difficult. We propose that where possible, the assignment and/or refinement of rule weights should be performed automatically. We present one approach to performing this training numerical optimization and report on the results of some preliminary tests in training rule bases. We also show that truth maintenance can be used to make the training more efficient and ask some epistemological questions raised by training rule weights. 1.0 THE NEED FOR TRAINING AB knowledge-based systems attempt to incorporate more of the evidential reason­ ing capabilities of human experts the adop­ tion of numerical representations for uncer­ tainty and imprecision has become more common. While the use of numerical representations does appear to allow better modeling of some aspects of human eviden­ tial reasoning, it also makes knowledge acquisition and system development, test, and modification more difficult. Experts have diffi culty translating their expertise into numerical terms. Almost universally they feel uncomfortable assigning and interpreting numerical weights. Ad hoc uncertainty representations make it impossi­ ble to objectively determine what weights should be given to even well understood aspects of the problem. Probability-based representations require experts to specify probabilities that they usually do not know. Moreover, failure of the assumptions required by probabilistic formalisms (e.g. independence) can make the acquired weights invalid in the context of the whole system despite their possible validity in iso­ lation. Most knowledge engineers admit to the necessity of modifying acquired rule weights until adequate system performance is obtained. Manual tuning is both time con­ suming and inexact. It is often based on inadequate tests and a relatively subjective "feel" of how the system is performing, and local improvements obtained by tuning one capability of the system are sometimes detri­ mental to other system capabilities. The automatic tuning of numerical weights in AI systems is not new [1-9]. Samuel [1,2] employed automatic tuning of coefficients in polynomial evaluation func* Part or this work was performed while the author was employed at GTE Government Systems, 100 Ferguson Rd., Mountain View, CA 94042.