Directional Influence Function: Estimating Training Data Influence in Constrained Learning

This paper proposes the Directional Influence Function (DIF) for estimating how perturbing or removing individual training samples changes solutions in constrained learning. DIF represents the optimality conditions of constrained optimization as a variational inequality and analyzes how data perturbations affect that inequality. The authors report evaluations on constrained linear regression and fairness-constrained CNNs. According to the abstract, DIF recovers leave-one-out retraining results more accurately than classical influence functions and penalty-based influence estimates, while better predicting test-loss changes after data removal.