Finding Most Influential Sets

• URL: http://arxiv.org/abs/2606.05919v2
• Date: Fri, 05 Jun 2026 08:44:55 GMT
• Title: Finding Most Influential Sets
• Abstract summary: Dinkelbach's method yields an algorithm with $mathcalO(n)$ cost per iteration and finite termination.<n>We show that the method recovers exact MIS that were previously computationally inaccessible.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-sa/4.0/
• 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.

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