PREDICTIVE INFERENCE WITH THE JACKKNIFE
PREDICTIVE INFERENCE WITH THE JACKKNIFE
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DOI：
10.1214/20-aos1965
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发表时间：
2021-02-01
影响因子：
4.5
通讯作者：
Tibshirani, Ryan J.
中科院分区：
文献类型：
--
作者：
Barber, Rina Foygel;Candes, Emmanuel J.;Tibshirani, Ryan J.
本文介绍了一种构造预测置信区间的新方法Jackknife+。jackknife输出一个以测试点的预测响应为中心的区间，区间的宽度由留一残差的分位数确定，而jackknife+也使用测试点的留一预测来解释拟合回归函数的变异性。假设可交换的训练样本，我们证明了这一重要的修改允许严格的覆盖率保证，无论数据点的分布，任何算法，对称地对待训练点。这样的保证是不可能的原始折刀，我们展示的例子中，覆盖率实际上可能会消失。我们的理论和实证分析表明，刀切和刀切+区间达到几乎精确的覆盖范围，并有类似的长度时，拟合算法服从某种形式的稳定性。此外，我们扩展了折刀+K折交叉验证，同样建立严格的覆盖属性。我们的方法与Vovk（Ann. Math. Artif.内特尔74（2015）9-28），我们讨论连接。
This paper introduces the jackknife+, which is a novel method for constructing predictive confidence intervals. Whereas the jackknife outputs an interval centered at the predicted response of a test point, with the width of the interval determined by the quantiles of leave-one-out residuals, the jackknife+ also uses the leave-one-out predictions at the test point to account for the variability in the fitted regression function. Assuming exchangeable training samples, we prove that this crucial modification permits rigorous coverage guarantees regardless of the distribution of the data points, for any algorithm that treats the training points symmetrically. Such guarantees are not possible for the original jackknife and we demonstrate examples where the coverage rate may actually vanish. Our theoretical and empirical analysis reveals that the jackknife and the jackknife+ intervals achieve nearly exact coverage and have similar lengths whenever the fitting algorithm obeys some form of stability. Further, we extend the jackknife+ to K-fold cross validation and similarly establish rigorous coverage properties. Our methods are related to cross-conformal prediction proposed by Vovk (Ann. Math. Artif. Intell. 74 (2015) 9-28) and we discuss connections.