A Sequential Sampling Algorithm for a General Class of Utility Criteria

Many discovery problems, e.g., subgroup or association rule discovery, can naturally be cast as n-best hypothesis problems where the goal is to nd the n hypotheses from a given hypothesis space that score best according to a given utility function. We present a sampling algorithm that solves this problem by issuing a small number of database queries while guaranteeing precise bounds on condence and quality of solutions. Known sampling algorithms assume that the utility be the average (over the examples) of some function, which is not the case for many frequently used utility functions. We show that our algorithm works for all utilities that can be estimated with bounded error. We provide such error bounds and resulting worst-case sample bounds for some of the most frequently used utilities, and prove that there is no sampling algorithm for another popular class of utility functions. The algorithm is sequential in the sense that it starts to return (or discard) hypotheses that already..