PreprintCC BY 4.0HAL
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 where the number of samples and data dimension diverge at proportional rates, 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.
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BibTeX
@misc{cui2026influence,
title = {{Influence Diagnostics in High-dimensional M-estimation: Precise Asymptotics}},
author = {Hugo Cui},
howpublished = {HAL},
year = {2026},
month = jul,
doi = {10.48550/arxiv.2607.09250},
eprint = {2607.09250},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05692586v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Influence Diagnostics in High-dimensional M-estimation: Precise Asymptotics
AU - Hugo Cui
PY - 2026
DA - 2026/07/10
PB - HAL
DO - 10.48550/arxiv.2607.09250
UR - https://hal.science/hal-05692586v1
AB - 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 where the number of samples and data dimension diverge at proportional rates, 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.
ER -