Generative Quantile Regression with Variability Penalty

Ray Bai (University of South Carolina)

Friday 9th December 15:00-16:00 Zoom


Quantile regression and conditional density estimation can often reveal structure that is missed by mean regression, such as heterogeneous subpopulations (i.e. multimodality) and skewness. In this talk, we introduce a deep learning generative model for simultaneous quantile regression called Penalized Generative Quantile Regression (PGQR). Our approach simultaneously generates samples from a large number of random quantile levels, thus allowing us to infer the conditional density of a response variable given a set of covariates. Our method also employs a novel variability penalty to avoid the common problem of vanishing variance in deep generative models. Furthermore, we introduce a new family of neural networks called partial monotonic neural networks (PMNN) to circumvent the problem of crossing quantile planes. A major benefit of PGQR is that our method 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.

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