  Research in both machine learning and psychology suggests that salient
examples can help humans to interpret learning models. To this end, we take a
novel look at black box interpretation of test predictions in terms of training
examples. Our goal is to ask `which training examples are most responsible for
a given set of predictions'? To answer this question, we make use of Fisher
kernels as the defining feature embedding of each data point, combined with
Sequential Bayesian Quadrature (SBQ) for efficient selection of examples. In
contrast to prior work, our method is able to seamlessly handle any sized
subset of test predictions in a principled way. We theoretically analyze our
approach, providing novel convergence bounds for SBQ over discrete candidate
atoms. Our approach recovers the application of influence functions for
interpretability as a special case yielding novel insights from this
connection. We also present applications of the proposed approach to three use
cases: cleaning training data, fixing mislabeled examples and data
summarization.
