Abstract
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.
