If Influence Functions are the Answer, Then What is the Question?
This work addresses the reliability of influence functions for practitioners in machine learning, particularly for model debugging and data analysis, by clarifying their limitations and proposing an alternative interpretation, though it is incremental in refining existing methods.
The paper investigates why influence function estimates, which measure the effect of removing a training point on model parameters, often poorly align with leave-one-out retraining in neural networks, decomposing the discrepancy into five terms and showing that these estimates approximate a different object called the proximal Bregman response function, which remains useful for tasks like identifying influential examples.
Influence functions efficiently estimate the effect of removing a single training data point on a model's learned parameters. While influence estimates align well with leave-one-out retraining for linear models, recent works have shown this alignment is often poor in neural networks. In this work, we investigate the specific factors that cause this discrepancy by decomposing it into five separate terms. We study the contributions of each term on a variety of architectures and datasets and how they vary with factors such as network width and training time. While practical influence function estimates may be a poor match to leave-one-out retraining for nonlinear networks, we show they are often a good approximation to a different object we term the proximal Bregman response function (PBRF). Since the PBRF can still be used to answer many of the questions motivating influence functions, such as identifying influential or mislabeled examples, our results suggest that current algorithms for influence function estimation give more informative results than previous error analyses would suggest.