Converting High-Dimensional Regression to High-Dimensional Conditional Density Estimation

Understand

There is a growing demand for nonparametric conditional density estimators (CDEs) in fields such as astronomy and economics.

• In astronomy, for example, one can dramatically improve estimates of the parameters that dictate the evolution of the Universe by working with full conditional densities instead of regression (i.e., conditional mean) estimates.
• More generally, standard regression falls short in any prediction problem where the distribution of the response is more complex with multi-modality, asymmetry or heteroscedastic noise.
• Nevertheless, much of the work on high-dimensional inference concerns regression and classification only, whereas research on density estimation has lagged behind.