CVaR锚定回归防御罕见偏移
CVaR anchor regression protects against rare shifts
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中文总结 AI 辅助
本研究提出CVaR锚定回归，通过尾部平均替代均值残差惩罚，在保留常见环境精度的同时，防御罕见大偏移，并给出最坏情况风险保证。
中文摘要 AI 辅助
我们研究了当训练数据包含罕见的大偏移时，在新环境中的预测问题。锚定回归惩罚了各环境间平方均值残差的平均值。它能够防御由训练偏移的二阶矩所确定的椭球体内的偏移。因此，覆盖罕见偏移可能需要较大的惩罚，这会在各个方向上扩大椭球体，并降低常见环境下的准确性。我们提出了CVaR锚定回归，该方法用尾部平均值替代平方均值残差的平均值。与直接应用于预测风险的CVaR或GroupDRO不同，它不会仅仅因为某些环境的噪声水平高而给予它们更多权重。我们在允许异方差噪声的线性结构模型下，证明了精确的最坏情况风险保证。对于离散环境，降低CVaR尾部比例会将鲁棒性集合从椭球体扩展为训练偏移及其负值的缩放凸包。一个单独的参数控制其规模。示例展示了该方法如何在保留常见环境准确性的同时，提升对罕见偏移的防御能力。我们在纽约市出租车数据上对该方法进行了说明。
英文摘要
We study prediction in new environments when training data contain rare, large shifts. Anchor regression penalizes the average of the squared mean residual across environments. It protects against shifts in an ellipsoid determined by the second moment of the training shifts. Covering rare shifts may therefore require a large penalty, expanding the ellipsoid in every direction and reducing accuracy on common environments. We propose CVaR anchor regression, which replaces the average of the squared mean residuals with a tail average. Unlike CVaR or GroupDRO applied directly to prediction risks, it does not give environments more weight solely because their noise levels are high. We prove an exact worst-case risk guarantee under a linear structural model that allows for heteroscedastic noise. For discrete environments, decreasing the CVaR tail fraction expands the robustness set from an ellipsoid to a scaled convex hull of the training shifts and their negatives. A separate parameter controls its scale. Examples show how the method can improve protection against rare shifts while retaining accuracy on common environments. We illustrate the method on New York City taxi data.
