Active Heteroscedastic Regression

An active learner is given a model classΘ, a large
sample of unlabeled data drawn from an underlying
distribution and access to a labeling oracle
that can provide a label for any of the unlabeled
instances. The goal of the learner is to find a
model θ ∈ Θ that fits the data to a given accuracy
while making as few label queries to the oracle as
possible. In this work, we consider a theoretical
analysis of the label requirement of active learning
for regression under a heteroscedastic noise
model, where the noise depends on the instance.
We provide bounds on the convergence rates of
active and passive learning for heteroscedastic
regression. Our results illustrate that just like
in binary classification, some partial knowledge
of the nature of the noise can lead to significant
gains in the label requirement of active learning.