On the Accuracy of Influence Functions for Measuring Group Effects
This addresses the problem of efficiently measuring group effects in large datasets for researchers and practitioners, but it is incremental as it builds on existing influence function methods.
The paper investigates whether influence functions, which estimate the effect of removing training points without retraining, remain accurate for large groups of points, such as for diagnosing batch effects. It finds that predicted effects correlate well with actual effects across various real-world datasets, though absolute and relative errors can be large, and theoretical analysis shows this accuracy depends on specific dataset properties.
Influence functions estimate the effect of removing a training point on a model without the need to retrain. They are based on a first-order Taylor approximation that is guaranteed to be accurate for sufficiently small changes to the model, and so are commonly used to study the effect of individual points in large datasets. However, we often want to study the effects of large groups of training points, e.g., to diagnose batch effects or apportion credit between different data sources. Removing such large groups can result in significant changes 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 a range of real-world datasets, the predicted effect (using influence functions) of a group correlates surprisingly well with its actual effect, even if the absolute and relative errors are large. Our theoretical analysis shows that such strong correlation arises only under certain settings and need not hold in general, indicating that real-world datasets have particular properties that allow the influence approximation to be accurate.