论文标题
贝叶斯正常模型的保留跨验估估计量的方差的无偏估计器
Unbiased estimator for the variance of the leave-one-out cross-validation estimator for a Bayesian normal model with fixed variance
论文作者
论文摘要
在使用剩余的交叉验证（LOO-CV）评估和比较模型时，通常使用采样分布的方差评估估计值的不确定性。考虑到不确定性很重要，因为在某些情况下估计的变异性可能很高。 Bengio和Grandvalet（2004）的重要结果指出，没有一般的无偏差估计器可以构建，可以适用于任何实用程序或损失度量和任何模型。我们表明，考虑特定的预测性能度量和模型，可以构建一个公正的估计器。我们使用预期的log Pointise预测密度（ELPD）实用程序得分证明了具有固定模型方差的贝叶斯正常模型的无偏采样分布方差估计器。该示例表明，可以获得改进，特定问题，公正的估计量来评估LOO-CV估计中的不确定性。
When evaluating and comparing models using leave-one-out cross-validation (LOO-CV), the uncertainty of the estimate is typically assessed using the variance of the sampling distribution. Considering the uncertainty is important, as the variability of the estimate can be high in some cases. An important result by Bengio and Grandvalet (2004) states that no general unbiased variance estimator can be constructed, that would apply for any utility or loss measure and any model. We show that it is possible to construct an unbiased estimator considering a specific predictive performance measure and model. We demonstrate an unbiased sampling distribution variance estimator for the Bayesian normal model with fixed model variance using the expected log pointwise predictive density (elpd) utility score. This example demonstrates that it is possible to obtain improved, problem-specific, unbiased estimators for assessing the uncertainty in LOO-CV estimation.
