张浩彬 (2022-08-23 15:36):
#paper doi: 10.1080/10618600.2021.1909601 Moon, S. J., Jeon, J.-J., Lee, J. S. H., & Kim, Y. (2021). Learning Multiple Quantiles With Neural Networks. Journal of Computational and Graphical Statistics, 30(4), 1238–1248. 提出了一个神经网络模型,用于估计满足非交叉属性的多个条件分位数。 传统的分位数回归会面临一个问题就是可能会出现分位数交叉,即85%分位数的值大于90%分位数的值。一般来说有两种处理策略:(1)调整转转模型参数;(2)将模型空间限制为非交叉分位数。本文采用了第二种思路,借鉴了线性非交叉分位数回归(非交叉SVR中的一个策略,这个策略问题在于计算量可能比较大),提出了一种具有不等式约束的非交叉分位数神经网络模型(把不等式约束用在了神经网络隐藏层)。 解决了交叉问题,第二个贡献是计算效率。为了使用一阶优化方法,文章开发了一种新算法来拟合所提出的模型。 该算法在没有需要多项式计算时间的投影梯度步骤的情况下给出了几乎最优的解决方案。
Learning Multiple Quantiles With Neural Networks
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Abstract:
We present a neural network model for estimation of multiple conditional quantiles that satisfies the noncrossing property. Motivated by linear noncrossing quantile regression, we propose a noncrossing quantile neural network model with inequality constraints. In particular, to use the first-order optimization method, we develop a new algorithm for fitting the proposed model. This algorithm gives a nearly optimal solution without the projected gradient step that requires polynomial computation time. We compare the performance of our proposed model with that of existing neural network models on simulated and real precipitation data. Supplementary materials for this article are available online.
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