论文标题
改进的共形分位数回归
Improved conformalized quantile regression
论文作者
论文摘要
共形分位回归是一种继承保形预测和分位回归的优势的程序。也就是说，我们使用分位数回归来估计真实条件分位数，然后在校准集合设置上采用共形步骤以确保边缘覆盖率。通过这种方式，我们获得了解释异质性的自适应预测间隔。然而，如（Romano等，2019）所述，上述形式缺乏适应性。为了克服这一限制，我们建议在估计条件分位数后使用分位数回归后应用单个共形步骤，而是建议将解释变量通过优化的k均值加权的解释变量聚集，并应用k形成步骤。为了证明此改进的版本优于共同的分位数回归的经典版本，并且更适合异方差，我们可以广泛比较开放数据集中两者的预测间隔。
Conformalized quantile regression is a procedure that inherits the advantages of conformal prediction and quantile regression. That is, we use quantile regression to estimate the true conditional quantile and then apply a conformal step on a calibration set to ensure marginal coverage. In this way, we get adaptive prediction intervals that account for heteroscedasticity. However, the aforementioned conformal step lacks adaptiveness as described in (Romano et al., 2019). To overcome this limitation, instead of applying a single conformal step after estimating conditional quantiles with quantile regression, we propose to cluster the explanatory variables weighted by their permutation importance with an optimized k-means and apply k conformal steps. To show that this improved version outperforms the classic version of conformalized quantile regression and is more adaptive to heteroscedasticity, we extensively compare the prediction intervals of both in open datasets.
