Influence Diagnostics in High-dimensional M-estimation: Precise Asymptotics

arXiv:2607.09250v2 Announce Type: replace-cross Abstract: The impact of a given training point on a statistical model can be measured through its leave-one-out influence on the model parameters, which quantifies how its removal from the training set affects the learned weights. For convex M-estimation under Gaussian design, in the high-dimensional limit nasymp d, we show that the empirical distribution of influences across training points concentrates around a deterministic measure which we sharply characterize. This characterization suggests that influential samples tend to lie on average close to the decision boundary, making contact with a standard data selection heuristic in active learning.

Source: arXiv cs.LG | 2026-09-28