Computing High-dimensional Confidence Sets for Arbitrary Distributions

We study the problem of learning a high-density region of an arbitrary distribution over $\mathbb{R}^d$. Given a target coverage parameter $\delta$, and sample access to an arbitrary distribution $D$, we want to output a confidence set $S \subset \mathbb{R}^d$ such that $S$ achieves $\delta$ coverage of $D$, i.e., $\mathbb{P}_{y \sim D} \left[ y \in S \right] \ge \delta$, and the volume of $S$ is as small as possible. This is a central problem in high-dimensional statistics with applications in finding confidence sets, uncertainty quantification, and support estimation.

@article{gao2025_2504.02723,
  title={ Computing High-dimensional Confidence Sets for Arbitrary Distributions },
  author={ Chao Gao and Liren Shan and Vaidehi Srinivas and Aravindan Vijayaraghavan },
  journal={arXiv preprint arXiv:2504.02723},
  year={ 2025 }
}