Abstract
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 language | American English |
|---|---|
| Article number | 9508166 |
| Pages (from-to) | 1680-1684 |
| Number of pages | 5 |
| Journal | IEEE Signal Processing Letters |
| Volume | 28 |
| DOIs | |
| State | Published - 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@ mail.huji.ac.il; galelidan@gmail.com; ami.wiesel@mail.huji.ac.il).
Publisher Copyright:
© 1994-2012 IEEE.
Keywords
- Linear regression
- convex optimization
- nonparanormal distribution