  A commonly observed pattern in machine learning models is an underprediction
of the target feature, with the model's predicted target rate for members of a
given category typically being lower than the actual target rate for members of
that category in the training set. This underprediction is usually larger for
members of minority groups; while income level is underpredicted for both men
and women in the 'adult' dataset, for example, the degree of underprediction is
significantly higher for women (a minority in that dataset). We propose that
this pattern of underprediction for minorities arises as a predictable
consequence of statistical inference on small samples. When presented with a
new individual for classification, an ML model performs inference not on the
entire training set, but on a subset that is in some way similar to the new
individual, with sizes of these subsets typically following a power law
distribution so that most are small (and with these subsets being necessarily
smaller for the minority group). We show that such inference on small samples
is subject to systematic and directional statistical bias, and that this bias
produces the observed patterns of underprediction seen in ML models. Analysing
a standard sklearn decision tree model's predictions on a set of over 70
subsets of the 'adult' and COMPAS datasets, we found that a bias prediction
measure based on small-sample inference had a significant positive correlations
(0.56 and 0.85) with the observed underprediction rate for these subsets.
