Generative Quantile Regression with Variability Penalty
提出一种深度学习生成模型PGQR，通过同时生成多个随机分位水平的样本并引入变异性惩罚和部分单调神经网络，解决分位数回归中的交叉曲线和变异性消失问题，适用于推断响应变量的条件分布。
Quantile regression and conditional density estimation can reveal structure that is missed by mean regression, such as multimodality and skewness. In this article, we introduce a deep learning generative model for joint quantile estimation called Penalized Generative Quantile Regression (PGQR). Our approach simultaneously generates samples from many random quantile levels, allowing us to infer the conditional distribution of a response variable given a set of covariates. Our method employs a novel variability penalty to avoid the problem of vanishing variability, or memorization, in deep generative models. Further, we introduce a new family of partial monotonic neural networks (PMNN) to circumvent the problem of crossing quantile curves. A major benefit of PGQR is that it can be fit using a single optimization, thus, bypassing the need to repeatedly train the model at multiple quantile levels or use computationally expensive cross-validation to tune the penalty parameter. We illustrate the efficacy of PGQR through extensive simulation studies and analysis of real datasets. Code to implement our method is available at https://github.com/shijiew97/PGQR.