Convex Nonparanormal Regression

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