Convex Nonparanormal Regression

Yonatan Woodbridge*, Gal Elidan, Ami Wiesel

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Quantifying uncertainty in predictions or, more generally, estimating the posterior conditional distribution, is a core challenge in machine learning and statistics. We introduce Convex Nonparanormal Regression (CNR), a conditional nonparanormal approach for coping with this task. CNR involves a convex optimization of a posterior defined via a rich dictionary of pre-defined non linear transformations on Gaussians. It can fit an arbitrary conditional distribution, including multimodal and non-symmetric posteriors. For the special but powerful case of a piecewise linear dictionary, we provide a closed form of the posterior mean which can be used for point-wise predictions. Finally, we demonstrate the advantages of CNR over classical competitors using synthetic and real world data.

Original languageAmerican English
Article number9508166
Pages (from-to)1680-1684
Number of pages5
JournalIEEE Signal Processing Letters
StatePublished - 2021

Bibliographical note

Funding Information:
Manuscript received December 9, 2020; revised July 13, 2021; accepted July 30, 2021. Date of publication August 5, 2021; date of current version August 30, 2021. This work was supported in part by the Israel Science Foundation (ISF) under Grant 1339/15. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Nelly Pustelnik. (Corresponding author: Yonatan Woodbridge.) The authors are with the Hebrew University of Jerusalem, Jerusalem 91905, Israel, and also with Google Research (e-mail: yonatan.woodbridge@;;

Publisher Copyright:
© 1994-2012 IEEE.


  • Linear regression
  • convex optimization
  • nonparanormal distribution


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