Version Space Completeness for Novel Hypothesis Induction in Biomedical Applications

Abstract

Use of traditional discretization methods caused a heavy loss of hypotheses in the induction of version spaces. We present a new discretization method, named two-point discretization, to construct an interval covering all the positive data points of a variable as purely as possible. We prove that the two-point discretization is a necessary and sufficient condition to guarantee the completeness of version spaces (i.e., no loss of hypothesis). A linear complexity algorithm is proposed to implement these theories. The algorithm is also applied to real-world bioinformatics problems to induce significant biomedical hypotheses which have been never discovered by the traditional approaches.