On the Accuracy of Influence Functions for Measuring Group Effects

TL;DR

This paper investigates the accuracy of influence functions in estimating the effects of large groups of training points on models, revealing they often correlate well with actual effects in real-world datasets despite potential errors.

Contribution

The study extends influence function analysis from individual points to large groups, providing empirical evidence and theoretical insights into their accuracy in real-world scenarios.

Findings

Influence functions often correlate well with actual group effects in practice.

Theoretical analysis explains conditions under which influence functions are accurate.

Real-world datasets possess properties that support the effectiveness of influence approximations.

Abstract

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.