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

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 $n\asymp d$, 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.

Machine Learning (stat.ML); Machine Learning (cs.LG)

arXiv:2607.09250 [stat.ML]

(or arXiv:2607.09250v2 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2607.09250 Focus to learn more arXiv-issued DOI via DataCite

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