Quantifying Prior Determination Knowledge Using the PAC Learning Model

Abstract

Prior knowledge, or bias, regarding a concept can reduce the number of examples needed to learn it. Probably Approximately Correct (PAC) learning is a mathematical model of concept learning that can be used to quantify the reduction in the number of examples due to different forms of bias. Thus far, PAC learning has mostly been used to analyze syntactic bias, such as limiting concepts to conjunctions of boolean prepositions. This paper demonstrates that PAC learning can also be used to analyze semantic bias, such as a domain theory about the concept being learned. The key idea is to view the hypothesis space in PAC learning as that consistent with all prior knowledge, syntactic and semantic. In particular, the paper presents an analysis of determinations, a type of relevance knowledge. The results of the analysis reveal crisp distinctions and relations among different determinations, and illustrate the usefulness of an analysis based on the PAC learning model.