{"ID":3083921,"CreatedAt":"2026-06-05T06:46:15.197025399Z","UpdatedAt":"2026-06-07T06:05:08.191440377Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.05919","arxiv_id":"2606.05919","title":"Finding Most Influential Sets","abstract":"Identifying most influential sets (MIS) - size-$k$ subsets whose removal maximally changes a target estimand - is typically infeasible because it requires searching over $\\binom{n}{k}$ subsets. For estimands with linear-fractional leave-set-out effects, we show that MIS selection reduces to a one-parameter sequence of top-$k$ problems. Dinkelbach's method yields an algorithm with $\\mathcal{O}(n)$ cost per iteration and finite termination. For fixed residualized inputs, the algorithm returns a globally optimal set for the univariate ratio objective, including the oracle-residualized partial linear model. With estimated nuisance functions, uniform denominator and generated-score stability imply approximation to the first-order oracle orthogonal-score objective; exact set recovery follows under a separation condition. Simulations and applications show that the method recovers exact MIS that were previously computationally inaccessible.","short_abstract":"Identifying most influential sets (MIS) - size-$k$ subsets whose removal maximally changes a target estimand - is typically infeasible because it requires searching over $\\binom{n}{k}$ subsets. For estimands with linear-fractional leave-set-out effects, we show that MIS selection reduces to a one-parameter sequence of...","url_abs":"https://arxiv.org/abs/2606.05919","url_pdf":"https://arxiv.org/pdf/2606.05919v1","authors":"[\"Lucas D. Konrad\",\"Nikolas Kuschnig\"]","published":"2026-06-04T09:24:26Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\",\"econ.EM\",\"stat.CO\"]","methods":"[]","has_code":false}