Multivariate Uncertainty Quantification with Tomographic Quantile Forests

doi:10.3390/mca31020053

Multivariate Uncertainty Quantification with Tomographic Quantile Forests

2026-04-01

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Kanazawa, Takuya *

DOI：10.3390/mca31020053

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Quantifying predictive uncertainty is essential for safe and trustworthy real-world AI deployment. However, the 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 n inverted perpendicular y as functions of the input x and the direction 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 to reconstruct the full conditional distribution itself, naturally overcoming any convexity restrictions. We evaluate TQF on synthetic and real-world datasets, and release the source code on GitHub.

Keywords:

random forest

uncertainty quantification

probabilistic prediction

tomography

quantile regression

Multivariate Uncertainty Quantification with Tomographic Quantile Forests

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