  Sampling biases in training data are a major source of algorithmic biases in
machine learning systems. Although there are many methods that attempt to
mitigate such algorithmic biases during training, the most direct and obvious
way is simply collecting more representative training data. In this paper, we
consider the task of assembling a training dataset in which minority groups are
adequately represented from a given set of data sources. In essence, this is an
adaptive sampling problem to determine if a given point lies in the convex hull
of the means from a set of unknown distributions. We present adaptive sampling
methods to determine, with high confidence, whether it is possible to assemble
a representative dataset from the given data sources. We also demonstrate the
efficacy of our policies in simulations in the Bernoulli and a multinomial
setting.
