论文标题
预测间隔，在异性高斯回归中具有控制长度
Prediction intervals with controlled length in the heteroscedastic Gaussian regression
论文作者
论文摘要
我们解决了在异质的高斯回归中建立预测间隔的问题。我们专注于预期长度有限的预测间隔，以确保输出的解释性。在此框架中，我们得出了最佳预测间隔的封闭形式表达式，该表达式允许开发基于插件的数据驱动预测间隔。所提出的算法的构建基于两个样品，一个标记，另一个标记为未标记。在轻度条件下，我们表明我们的过程在预期长度和错误率方面渐近与最佳预测间隔一样好。特别是，对预期长度的控制是无分布的。我们还得出了在平滑度和Tsybakov噪声条件下的收敛速率。 我们进行了数值分析，表现出我们方法的良好性能。这也表明，即使使用了一些未标记的数据，我们的方法在执行长度约束方面也非常有效。
We tackle the problem of building a prediction interval in heteroscedastic Gaussian regression. We focus on prediction intervals with constrained expected length in order to guarantee interpretability of the output. In this framework, we derive a closed form expression of the optimal prediction interval that allows for the development a data-driven prediction interval based on plug-in. The construction of the proposed algorithm is based on two samples, one labeled and another unlabeled. Under mild conditions, we show that our procedure is asymptotically as good as the optimal prediction interval both in terms of expected length and error rate. In particular, the control of the expected length is distribution-free. We also derive rates of convergence under smoothness and the Tsybakov noise conditions. We conduct a numerical analysis that exhibits the good performance of our method. It also indicates that even with a few amount of unlabeled data, our method is very effective in enforcing the length constraint.
