Neural Optimal Transport Meets Multivariate Conformal Prediction
This work addresses the problem of constructing tighter and more informative predictive regions for multivariate responses in conformal prediction, which is incremental by combining existing techniques in a novel way.
The paper tackles the challenge of multivariate quantile regression by proposing a conditional vector quantile regression framework that integrates neural optimal transport with amortized optimization, and applies it to multivariate conformal prediction to produce distribution-free predictive regions with improved coverage-efficiency trade-offs in experiments.
We propose a framework for conditional vector quantile regression (CVQR) that combines neural optimal transport with amortized optimization, and apply it to multivariate conformal prediction. Classical quantile regression does not extend naturally to multivariate responses, while existing approaches often ignore the geometry of joint distributions. Our method parametrizes the conditional vector quantile function as the gradient of a convex potential implemented by an input-convex neural network, ensuring monotonicity and uniform ranks. To reduce the cost of solving high-dimensional variational problems, we introduced amortized optimization of the dual potentials, yielding efficient training and faster inference. We then exploit the induced multivariate ranks for conformal prediction, constructing distribution-free predictive regions with finite-sample validity. Unlike coordinatewise methods, our approach adapts to the geometry of the conditional distribution, producing tighter and more informative regions. Experiments on benchmark datasets show improved coverage-efficiency trade-offs compared to baselines, highlighting the benefits of integrating neural optimal transport with conformal prediction.