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This research provides precise asymptotic characterizations of influence diagnostics in high-dimensional convex M-estimation, revealing that influential samples typically reside near the decision boundary. These findings offer a rigorous theoretical foundation for data selection heuristics used in active learning and model robustness analysis. By quantifying how individual training points affect learned weights under Gaussian design, the work advances our understanding of statistical influence in modern machine learning regimes.
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 $n\asymp d$, 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.
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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