  A new type of robust estimation problem is introduced where the goal is to
recover a statistical model that has been corrupted after it has been estimated
from data. Methods are proposed for "repairing" the model using only the design
and not the response values used to fit the model in a supervised learning
setting. Theory is developed which reveals that two important ingredients are
necessary for model repair---the statistical model must be over-parameterized,
and the estimator must incorporate redundancy. In particular, estimators based
on stochastic gradient descent are seen to be well suited to model repair, but
sparse estimators are not in general repairable. After formulating the problem
and establishing a key technical lemma related to robust estimation, a series
of results are presented for repair of over-parameterized linear models, random
feature models, and artificial neural networks. Simulation studies are
presented that corroborate and illustrate the theoretical findings.
