Multivariate conditional density estimation with copulas

Abstract

Most machine learning regression models only yield single point estimations for the label of a new observation. However, when dealing with multi-modal or asymmetric distributions, a single point estimate is not enough to summarize the full uncertainty over such label. One solution for this case is to estimate the full conditional density function of the label given the features, which is more informative. For instance, this density can be used to compute probability regions rather than single point estimates. Conditional densities become especially useful when modelling multivariate responses, which is often the case in fields such as cosmology. Most well known conditional density estimators are too slow to be computed or do not generalize to multivariate-response settings. To minimize such problems, our method estimates multivariate densities using copula to aggregate estimates of univariate conditional densities given by the recent-developed FlexCode. We show that this solution leads to improved results when compared to other state-of-the-art techniques.