高效找出对统计估计影响最大的数据子集，突破传统计算瓶颈。
Finding Most Influential Sets
- 将问题转化为单参数序列的前k大选择，大幅降低搜索复杂度。
- 算法每轮仅需O(n)成本，可精确找到最优影响集合。
- 适用于高维回归、因果推断等场景，尤其适合处理敏感性分析。
识别最具影响力的集合（MIS）——即移除后使目标估计量变化最大的大小为k的子集——通常不可行，因需遍历组合数$\binom{n}{k}$。对于具有线性分式留集效应的估计量，我们证明MIS选择可简化为一参数序列的前k大问题。Dinkelbach方法实现每轮$\mathcal{O}(n)$复杂度，并保证有限终止。在残差输入固定时，算法可返回单变量比值目标的全局最优集合，包括基于真值残差的偏线性模型。当使用估计的扰动函数时，在分母一致性和生成得分稳定性条件下，逼近一阶正交得分目标；在分离条件下可实现精确集合恢复。模拟与实际应用表明，该方法能恢复此前计算上无法获得的精确MIS。
原文摘要 · Abstract (English)
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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