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.