Finding Most Influential Sets

arXiv:2606.05919v2 Announce Type: replace-cross Abstract: Identifying most influential sets (MIS) - size-k subsets whose removal maximally changes a target estimand - is typically infeasible because it requires searching over inom{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 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.

Source: arXiv cs.LG | 2026-06-08