{"ID":6497749,"CreatedAt":"2026-07-13T01:19:40.13847098Z","UpdatedAt":"2026-07-14T01:36:59.12045529Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.09250","arxiv_id":"2607.09250","title":"Influence Diagnostics in High-dimensional M-estimation: Precise Asymptotics","abstract":"The impact of a given training point on a statistical model is classically measured through its leave-one-out influence, which quantifies the effect of its removal from the training set on the model accuracy. While the statistics of leave-one-out influences are well understood in the low-dimensional, large sample limit $n\\to \\infty, d=O(1)$, they become more intricate in high dimensions, as the influence of a given sample develops non-trivial dependencies on all other training samples. For convex M-estimation under Gaussian design, in the high-dimensional limit $n\\asymp d$, we show that the distribution of the influences across the training set converges to a limiting measure which we sharply characterize. Building on these results, we provide evidence that influential samples tend to lie close to the decision boundary, thereby making contact with a standard data selection heuristic in active learning.","short_abstract":"The impact of a given training point on a statistical model is classically measured through its leave-one-out influence, which quantifies the effect of its removal from the training set on the model accuracy. While the statistics of leave-one-out influences are well understood in the low-dimensional, large sample limit...","url_abs":"https://arxiv.org/abs/2607.09250","url_pdf":"https://arxiv.org/pdf/2607.09250v1","authors":"[\"Hugo Cui\"]","published":"2026-07-10T10:01:11Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\"]","methods":"[]","has_code":false}