  The presence of spurious features interferes with the goal of obtaining
robust models that perform well across many groups within the population. A
natural remedy is to remove spurious features from the model. However, in this
work we show that removal of spurious features can decrease accuracy due to the
inductive biases of overparameterized models. We completely characterize how
the removal of spurious features affects accuracy across different groups (more
generally, test distributions) in noiseless overparameterized linear
regression. In addition, we show that removal of spurious feature can decrease
the accuracy even in balanced datasets -- each target co-occurs equally with
each spurious feature; and it can inadvertently make the model more susceptible
to other spurious features. Finally, we show that robust self-training can
remove spurious features without affecting the overall accuracy. Experiments on
the Toxic-Comment-Detectoin and CelebA datasets show that our results hold in
non-linear models.
