Convex Nonparanormal Regression
This addresses the problem of uncertainty estimation in machine learning and statistics, offering a novel approach for practitioners needing robust posterior distributions.
The paper tackles the challenge of quantifying uncertainty in predictions by introducing Convex Nonparanormal Regression (CNR), a method that fits arbitrary conditional distributions, including multimodal and non-symmetric ones, and demonstrates its advantages over classical competitors on synthetic and real-world data.
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.