Learning Multiple Quantiles With Neural Networks

Sang Jun Moon, Jong June Jeon, Jason Sang Hun Lee, Yongdai Kim

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


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.

Original languageEnglish
Pages (from-to)1238-1248
Number of pages11
JournalJournal of Computational and Graphical Statistics
Issue number4
StatePublished - 2021


  • Deep learning
  • Feed-forward neural network
  • Interior point algorithm
  • Projected gradient algorithm
  • Quantile regression


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