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Selecting Data to Minimize Learner Variance

In this paper we consider algorithms for active learning which select data in an attempt to minimize the value of Equation 4, integrated over X. Intuitively, the minimization proceeds as follows: we assume that we have an estimate of , the variance of the learner at x. If, for some new input , we knew the conditional distribution , we could compute an estimate of the learner's new variance at x given an additional example at . While the true distribution is unknown, many learning architectures let us approximate it by giving us estimates of its mean and variance. Using the estimated distribution of , we can estimate , the expected variance of the learner after querying at .

Given the estimate of , which applies to a given x and a given query , we must integrate x over the input distribution to compute the integrated average variance of the learner. In practice, we will compute a Monte Carlo approximation of this integral, evaluating at a number of reference points drawn according to . By querying an that minimizes the average expected variance over the reference points, we have a solid statistical basis for choosing new examples.

David Cohn
Mon Mar 25 09:20:31 EST 1996