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Neural Optimal Transport Meets Multivariate Conformal Prediction

ICLR 2026

Quantile figure 0 Quantile figure 1

Figure: Examples of multidimensional quantiles. Green dots represent the median prediction. Red dots are ground truth movement of a person. Red density estimate is density of possible movements estimated with the trained quantile function.

The notion of a quantile plays a central role in the one-dimensional setting. However, its extension to higher dimensions is nontrivial. Recent approaches propose constructing multivariate quantiles within an optimal transport framework. In this project, we explore a numerical approach to realizing such quantile functions using convex neural networks.

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