Title: Adaptive Sampling Methods for Scaling up Knowledge Discovery Algorithms (extended Revised Version of Tr-c131)

Scalability is a key requirement for any KDD and data mining algorithm, and one of the biggest research challenges is to develop methods that allow to use large amounts of data. One possible approach for dealing with huge amounts of data is to take a random sample and do data mining on it, since for many data mining applications approximate answers are acceptable. However, as argued by several researchers, random sampling is diicult to use due to the diiculty of determining an appropriate sample size. In this paper, we take a sequential sampling approach for solving this diiculty, and propose an adaptive sampling method that solves a general problem covering many actual problems arising in applications of discovery science. An algorithm following this method obtains examples sequentially in an on-line fashion, and it determines from the obtained examples whether it has already seen a large enough number of examples. Thus, sample size is not xed a priori; instead, it adaptively depends on the situation. Due to this adaptiveness, if we are not in a worst case situation as fortunately happens in many practical applications, then we can solve the problem with a number of examples much smaller than the required in the worst case. We prove the correctness of our method and estimates its eeciency theoretically. For illustrating its usefulness, we consider one concrete example of using sampling, provide an algorithm based on our method, and show its eeciency by experimental evaluation. (This an extended revised version of TR-C131.)