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.
翻译:共成孔径回归是一种继承符合预测和四分位回归的优势的程序。 也就是说, 我们使用四分位回归来估计真实的有条件的孔径, 然后在校准设置上应用一个符合的步数来确保边际覆盖。 这样, 我们得到适应性预测间隔, 算得上异质性。 但是, 如( Romano 等人, 2019 ) 所述, 上述符合性步骤缺乏适应性。 为了克服这一限制, 而不是在用量化回归来估计有条件的孔径后采取单一的一致步数, 我们提议用最优化的 k- 表示法将按其变异重要性加权的解释变量分组起来, 并应用 k 符合性步骤 。 要显示这个改进的版本超越了典型的正态的正态孔径回归, 并且更适应性。 我们广泛比较开放数据集中的两种预测间隔。