Multivariate Uncertainty Quantification with Tomographic Quantile Forests
This addresses the problem of multivariate uncertainty quantification for safe AI deployment, offering a novel method for a known bottleneck.
The paper tackles the challenge of nonparametric estimation of conditional distributions for multivariate targets by proposing Tomographic Quantile Forests (TQF), which learns conditional quantiles of directional projections and reconstructs distributions via sliced Wasserstein distance minimization, achieving efficient coverage of all directions without convexity restrictions.
Quantifying predictive uncertainty is essential for safe and trustworthy real-world AI deployment. Yet, fully nonparametric estimation of conditional distributions remains challenging for multivariate targets. We propose Tomographic Quantile Forests (TQF), a nonparametric, uncertainty-aware, tree-based regression model for multivariate targets. TQF learns conditional quantiles of directional projections $\mathbf{n}^{\top}\mathbf{y}$ as functions of the input $\mathbf{x}$ and the unit direction $\mathbf{n}$. At inference, it aggregates quantiles across many directions and reconstructs the multivariate conditional distribution by minimizing the sliced Wasserstein distance via an efficient alternating scheme with convex subproblems. Unlike classical directional-quantile approaches that typically produce only convex quantile regions and require training separate models for different directions, TQF covers all directions with a single model without imposing convexity restrictions. We evaluate TQF on synthetic and real-world datasets, and release the source code on GitHub.