  In NLP, recent work has seen increased focus on spurious correlations between
various features and labels in training data, and how these influence model
behavior. However, the presence and effect of such correlations are typically
examined feature by feature. We investigate the cumulative impact on a model of
many such intersecting features. Using a new statistical method, we examine
whether such spurious patterns in data appear in models trained on the data. We
select two tasks -- natural language inference and duplicate-question detection
-- for which any unigram feature on its own should ideally be uninformative,
which gives us a large pool of automatically extracted features with which to
experiment. The large size of this pool allows us to investigate the
intersection of features spuriously associated with (potentially different)
labels. We then apply an optimization approach to *reweight* the training data,
reducing thousands of spurious correlations, and examine how doing so affects
models trained on the reweighted data. Surprisingly, though this method can
successfully reduce lexical biases in the training data, we still find strong
evidence of corresponding bias in the trained models, including worsened bias
for slightly more complex features (bigrams). We close with discussion about
the implications of our results on what it means to "debias" training data, and
how issues of data quality can affect model bias.
