  As machine learning is increasingly deployed in the real world, it is
paramount that we develop the tools necessary to analyze the decision-making of
the models we train and deploy to end-users. Recently, researchers have shown
that influence functions, a statistical measure of sample impact, can
approximate the effects of training samples on classification accuracy for deep
neural networks. However, this prior work only applies to supervised learning,
where training and testing share an objective function. No approaches currently
exist for estimating the influence of unsupervised training examples for deep
learning models. To bring explainability to unsupervised and semi-supervised
training regimes, we derive the first theoretical and empirical demonstration
that influence functions can be extended to handle mismatched training and
testing (i.e., "cross-loss") settings. Our formulation enables us to compute
the influence in an unsupervised learning setup, explain cluster memberships,
and identify and augment biases in language models. Our experiments show that
our cross-loss influence estimates even exceed matched-objective influence
estimation relative to ground-truth sample impact.
