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Finding Most Influential Sets

Author

Listed:
  • Lucas D. Konrad
  • Nikolas Kuschnig

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.

Suggested Citation

  • Lucas D. Konrad & Nikolas Kuschnig, 2026. "Finding Most Influential Sets," Papers 2606.05919, arXiv.org, revised Jun 2026.
    • Handle: RePEc:arx:papers:2606.05919
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    References listed on IDEAS

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