Quantile regression has a natural extension to generative modelling by leveraging a
stronger pointwise convergence than in distribution. While the pinball quantile loss works
well in the scalar case, it cannot be readily extended to the vector case. In this work, we
propose a multivariate quantile approach for generative modelling using optimal transport
with provable guarantees. Specifically, we suggest that by optimizing smooth functions
parameterized by neural networks with respect to the dual of the correlation maximization …

Quantile regression has a natural extension to generative modelling by leveraging a
stronger convergence in pointwise rather than in distribution. While the pinball quantile loss
works in the scalar case, it does not have a provable extension to the vector case. In this
work, we consider a quantile approach to generative modelling using optimal transport with
provable guarantees. We suggest and prove that by optimizing smooth functions with
respect to the dual of the correlation maximization problem, the optimum is convex almost …