Abstract: Many discovery problems, e.g., subgroup or association rule discovery, can naturally be cast as n-best hypotheses problems where the goal is to find the n hypotheses from a given hypothesis space that score best according to a certain utility function. We present a sampling algorithm that solves this problem by issuing a small number of database queries while guaranteeing precise bounds on confidence and quality of solutions. Known sampling approaches have treated single hypothesis selection problems, assuming 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 these 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 a popular class of utility functions that cannot be estimated with bounded error.

Abstract: Many discovery problems, e.g., subgroup or association rule discovery, can naturally be cast as n-best hypotheses problems where the goal is to find the n hypotheses from a given hypothesis space that score best according to a certain utility function. We present a sampling algorithm that solves this problem by issuing a small number of database queries while guaranteeing precise bounds on confidence and quality of solutions. Known sampling approaches have treated single hypothesis selection problems, assuming 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 these 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 a popular class of utility functions that cannot be estimated with bounded error.