Deep support vector quantile regression with non-crossing constraints

Wooyoung Shin, Yoonsuh Jung

Research output: Contribution to journalArticlepeer-review


We propose a new nonparametric regression approach that combines deep neural networks with support vector quantile regression models. The nature of deep neural networks enables complex nonlinear regression quantiles to be estimated more accurately. Because deep learning models have a complicated structure, the proposed method can easily fit both smooth and non-smooth data sets. For this reason, we can effectively model data sets with truncated points or locally different smoothness in which spline-based smoothing methods often fail. Stepwise fitting is used to increase computing speed when fitting multiple quantiles. This produces stable fits, especially when observations are scarce near the target quantile. In addition, we employ certain constraints to prevent the fitted quantiles from crossing. The benefits of the proposed method are more apparent when the errors are heteroscedastic, although quantile regression does not require homogeneous errors. We illustrate the flexibility of the proposed method using simulated data sets and six real data examples with univariate and multivariate input variables.

Original languageEnglish
Pages (from-to)1947-1976
Number of pages30
JournalComputational Statistics
Issue number4
Publication statusPublished - 2023 Dec

Bibliographical note

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.


  • Deep learning
  • Extreme quantiles
  • Neural networks
  • Quantile regression
  • SVM

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Computational Mathematics


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