Outlier detection by logic programming

Abstract

The development of effective knowledge discovery techniques has become a very active research area in recent years due to the important impact it has had in several relevant application domains. One interesting task therein is that of singling out anomalous individuals from a given population, for example, to detect rare events in time-series analysis settings, or to identify objects whose behavior is deviant w.r.t. a codified standard set of rules. Such exceptional individuals are usually referred to as outliers in the literature. In this article, the concept of outlier is formally stated in the context of knowledge-based systems, by generalizing that originally proposed in Angiulli et al. [2003] in the context of default theories. The chosen formal framework here is that of logic programming, wherein potential applications of techniques for outlier detection are thoroughly discussed. The proposed formalization is a novel one and helps to shed light on the nature of outliers occurring in logic bases. Also the exploitation of minimality criteria in outlier detection is illustrated. The computational complexity of outlier detection problems arising in this novel setting is also thoroughly investigated and accounted for in the paper. Finally, rewriting algorithms are proposed that transform any outlier detection problem into an equivalent inference problem under stable model semantics, thereby making outlier computation effective and realizable on top of any stable model solver.