  Several pool-based active learning algorithms were employed to model
potential energy surfaces (PESs) with a minimum number of electronic structure
calculations. Among these algorithms, the class of uncertainty-based algorithms
are popular. Their key principle is to query molecular structures corresponding
to high uncertainties in their predictions. We empirically show that this
strategy is not optimal for nonuniform data distributions as it collects many
structures from sparsely sampled regions, which are less important to
applications of the PES. We exploit a simple stochastic algorithm to correct
for this behavior and implement it using regression trees, which have
relatively small computational costs. We show that this algorithm requires
around half the data to converge to the same accuracy than the
uncertainty-based algorithm query-by-committee. Simulations on a 6D PES of
pyrrole(H$_2$O) show that $< 15\,000$ configurations are enough to build a PES
with a generalization error of $16$ cm$^{-1}$, whereas the final model with
around $50\,000$ configurations has a generalization error of $11$ cm$^{-1}$.
