On Second-Order Group Influence Functions for Black-Box Predictions
This work addresses the need for explainability in machine learning systems used in sensitive applications, offering an incremental improvement over existing influence function methods.
The paper tackles the problem of identifying influential groups of training samples for black-box model predictions by proposing second-order influence functions, which improve correlation with ground truth values and enhance group selection compared to first-order approximations.
With the rapid adoption of machine learning systems in sensitive applications, there is an increasing need to make black-box models explainable. Often we want to identify an influential group of training samples in a particular test prediction for a given machine learning model. Existing influence functions tackle this problem by using first-order approximations of the effect of removing a sample from the training set on model parameters. To compute the influence of a group of training samples (rather than an individual point) in model predictions, the change in optimal model parameters after removing that group from the training set can be large. Thus, in such cases, the first-order approximation can be loose. In this paper, we address this issue and propose second-order influence functions for identifying influential groups in test-time predictions. For linear models, across different sizes and types of groups, we show that using the proposed second-order influence function improves the correlation between the computed influence values and the ground truth ones. We also show that second-order influence functions could be used with optimization techniques to improve the selection of the most influential group for a test-sample.