We investigate practical algorithms to find or disprove the existence of
small subsets of a dataset which, when removed, reverse the sign of a
coefficient in an ordinary least squares regression involving that dataset. We
empirically study the performance of well-established algorithmic techniques
for this task -- mixed integer quadratically constrained optimization for
general linear regression problems and exact greedy methods for special cases.
We show that these methods largely outperform the state of the art and provide
a useful robustness check for regression problems in a few dimensions. However,
significant computational bottlenecks remain, especially for the important task
of disproving the existence of such small sets of influential samples for
regression problems of dimension $3$ or greater. We make some headway on this
challenge via a spectral algorithm using ideas drawn from recent innovations in
algorithmic robust statistics. We summarize the limitations of known techniques
in several challenge datasets to encourage further algorithmic innovation.

探讨了在普通最小二乘回归中，找到或推翻删除数据集中的小子集会反转系数符号的实用算法；通过实证研究了用于此任务的成熟算法技术在一般线性回归问题和特殊情况下的精确贪婪方法方面的性能，证明这些方法在几个维度的回归问题中优于现有技术并提供了实用的鲁棒性检查；但对于维度为 3 或更高的回归问题中推翻这种小型影响样本存在性的重要任务仍存在显著的计算瓶颈；通过使用源自算法稳健统计的最新创新思想的谱算法在这一挑战中取得了一些进展；总结了在几个挑战数据集中，已知技术的限制，以促进进一步的算法创新。