Fast Calibrated Additive Quantile Regression
Fast Calibrated Additive Quantile Regression
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DOI：
10.1080/01621459.2020.1725521
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发表时间：
2020-03-10
影响因子：
3.7
通讯作者：
Goude, Yannig
中科院分区：
文献类型：
--
作者：
Fasiolo, Matteo;Wood, Simon N.;Goude, Yannig
我们提出了一种新的框架拟合添加剂分位数回归模型，它提供了良好的校准推断的条件分位数和快速自动估计的平滑参数，模型结构不同的分布广义加性模型，同时保持同等的数值效率和稳定性。所提出的方法是在一次统计上严格和计算效率，因为它们是基于一般的信念更新框架的Bissiri，Holmes和步行者的损失为基础的推理，但计算通过适应稳定的拟合方法的木材，Pya和Safken。我们展示了弹球损失是如何统计次优相对于一个新的平滑推广，这也提供了快速估计方法。此外，我们提供了一种新的校准方法，有效地选择“学习率”平衡损失与平滑先验在推理过程中，从而获得可靠的分位数不确定性估计。我们的工作是出于概率电力负荷预测的应用程序，在这里使用，以证明所提出的方法。这里描述的方法是由qgam R包实现的，可以在Comprehensive R Archive Network（CRAN）上找到。可以在网上找到。
We propose a novel framework for fitting additive quantile regression models, which provides well-calibrated inference about the conditional quantiles and fast automatic estimation of the smoothing parameters, for model structures as diverse as those usable with distributional generalized additive models, while maintaining equivalent numerical efficiency and stability. The proposed methods are at once statistically rigorous and computationally efficient, because they are based on the general belief updating framework of Bissiri, Holmes, and Walker to loss based inference, but compute by adapting the stable fitting methods of Wood, Pya, and Safken. We show how the pinball loss is statistically suboptimal relative to a novel smooth generalization, which also gives access to fast estimation methods. Further, we provide a novel calibration method for efficiently selecting the "learning rate" balancing the loss with the smoothing priors during inference, thereby obtaining reliable quantile uncertainty estimates. Our work was motivated by a probabilistic electricity load forecasting application, used here to demonstrate the proposed approach. The methods described here are implemented by the qgam R package, available on the Comprehensive R Archive Network (CRAN). for this article are available online.