Fast Nonlinear Vector Quantile Regression. (arXiv:2205.14977v2 [stat.CO] UPDATED)

Quantile regression (QR) is a powerful tool for estimating one or more
conditional quantiles of a target variable $\mathrm{Y}$ given explanatory
features $\boldsymbol{\mathrm{X}}$. A limitation of QR is that it is only
defined for scalar target variables, due to the formulation of its objective
function, and since the notion of quantiles has no standard definition for
multivariate distributions. Recently, vector quantile regression (VQR) was
proposed as an extension of QR for vector-valued target variables, thanks to a
meaningful generalization of …

arxiv quantile regression vector