一种可同时处理多维输出不确定性的树模型，能高效构建非凸分布。
Multivariate Uncertainty Quantification with Tomographic Quantile Forests
- 基于方向性分位数学习，用单个模型覆盖所有方向的预测不确定性。
- 通过最小化切片沃尔什距离重构多维条件分布，精度优于传统方法。
- 适合需要高置信度多维预测的场景，如自动驾驶与金融风险建模。
准确量化预测不确定性对实现安全可信的现实世界人工智能部署至关重要。然而，对于多维目标，完全非参数化的条件分布估计仍具挑战性。我们提出了一种名为张量投影分位数森林（Tomographic Quantile Forest, TQF）的非参数、不确定性感知的树基回归模型，适用于多维目标。TQF将输入\mathbf{x}和单位方向\mathbf{n}作为条件，学习方向投影\mathbf{n}^\top\mathbf{y}的条件分位数。推理阶段，它在多个方向上聚合分位数，并通过高效的交替优化算法最小化切片沃尔什距离来重构多维条件分布，该算法具有凸子问题。与传统方向分位数方法通常仅生成凸分位数区域且需为不同方向训练独立模型不同，TQF使用单一模型即可覆盖所有方向，无需施加凸性限制。我们在合成数据集和真实数据集上评估了TQF的性能，并在GitHub上发布了源代码。
原文摘要 · Abstract (English)
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.
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