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Influence functions estimate the effect of removing a training point on amodel without the need to retrain. They are based on a first-order Taylorapproximation that is guaranteed to be accurate for sufficiently small changesto the model, and so are commonly used to study the effect of individual pointsin large datasets. However, we often want to study the effects of large groupsof training points, e.g., to diagnose batch effects or apportion credit betweendifferent data sources. Removing such large groups can result in significantchanges to the model. Are influence functions still accurate in this setting?In this paper, we find that across many different types of groups and for arange of real-world datasets, the predicted effect (using influence functions)of a group correlates surprisingly well with its actual effect, even if theabsolute and relative errors are large. Our theoretical analysis shows thatsuch strong correlation arises only under certain settings and need not hold ingeneral, indicating that real-world datasets have particular properties thatallow the influence approximation to be accurate.

On the Accuracy of Influence Functions for Measuring Group Effects