Finding Relevant Variables in PAC Model with Membership Queries

A new research frontier in AI and data mining seeks to develop methods to automatically discover relevant variables among many irrelevant ones. In this paper, we present four algorithms that output such crucial variables in PAC model with membership queries. The rst algorithm executes the task under any unknown distribution by measuring the distance between virtual and real targets. The second algorithm exhausts virtual version space under an arbitrary distribution. The third algorithm exhausts universal set under the uniform distribution. The fourth algorithm measures innuence of variables under the uniform distribution. Knowing the number r of relevant variables, the rst algorithm runs in almost linear time for r. The second and the third ones use less membership queries than the rst one, but runs in time exponential for r. The fourth one enumerates highly innuential variables in quadratic time for r.