Understanding Black-box Predictions via Influence Functions

This paper addresses how to explain the predictions of a black-box model by using influence functions, a classic technique from robust statistics. Influence functions trace a model's prediction back through the learning algorithm to the training data, identifying which training points are most responsible for a given prediction. To make this practical in modern machine learning settings, the authors develop a simple and efficient implementation that requires only oracle access to gradients and Hessian-vector products, allowing the method to scale beyond its classical theoretical setting.

The authors show that even on non-convex and non-differentiable models, where the underlying theory formally breaks down, approximations to influence functions still yield valuable information. Demonstrated on linear models and convolutional neural networks, the technique proves useful for multiple purposes, including understanding model behavior, debugging models, detecting dataset errors, and even creating visually indistinguishable training-set attacks. This mattered because it gave practitioners a principled, tractable tool for interpreting and diagnosing complex models through their training data.