# Inverse set estimation and inversion of simultaneous confidence intervals

arXiv: https://arxiv.org/abs/2210.03933 · HTML: https://mlsanity.com/paper/2210.03933/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Oct 2022.

## Built on by (most cited first, 1 of 1)

- [Model uncertainty quantification using feature confidence sets for outcome excursions](https://mlsanity.com/paper/2504.19464/) (2025)

## Abstract (arXiv)

Motivated by the questions of risk assessment in climatology (temperature change in North America) and medicine (impact of statin usage and COVID-19 on hospitalized patients), we address the problem of estimating the set in the domain of a function whose image equals a predefined subset. Existing methods that construct confidence sets require strict assumptions. We generalize the estimation of such sets to dense and non-dense domains with protection against "data peeking" by proving that confidence sets of multiple levels can be simultaneously constructed with the desired confidence non-asymptotically through inverting simultaneous confidence bands. A non-parametric bootstrap algorithm and code are provided.