# Selection from Hierarchical Data with Conformal e-values

arXiv: https://arxiv.org/abs/2501.02514 · HTML: https://mlsanity.com/paper/2501.02514/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jan 2025.

## Built on by (most cited first, 7 of 7)

- [WATCH: Adaptive Monitoring for AI Deployments via Weighted-Conformal Martingales](https://mlsanity.com/paper/2505.04608/) (2025)
- [Conformal Selective Prediction with General Risk Control](https://mlsanity.com/paper/2603.24704/) (2026)
- [Multi-Condition Conformal Selection](https://mlsanity.com/paper/2510.08075/) (2025)
- [Fuzzy Prediction Sets: Conformal Prediction with E-values](https://mlsanity.com/paper/2509.13130/) (2025)
- [Beyond Fixed False Discovery Rates: Post-Hoc Conformal Selection with E-Variables](https://mlsanity.com/paper/2604.11305/) (2026)
- [Self-Poisoning in Adaptive Out-of-Distribution Detection: A Sharp-Threshold Theory and Certified Label-Free Calibration](https://mlsanity.com/paper/2607.21673/) (2026)
- [Robust Conformalized Selection with Noisy Responses](https://mlsanity.com/paper/2607.22985/) (2026)

## Abstract (arXiv)

Distribution-free predictive inference beyond the construction of prediction sets has gained a lot of interest in recent applications. One such application is the selection task, where the objective is to design a reliable selection rule to pick out individuals with desired unobserved outcomes while controlling the error rate. In this work, we address the selection problem in the context of hierarchical data, where groups of observations may exhibit distinct within-group distributions. This generalizes existing techniques beyond the standard i.i.d./exchangeable data settings. As a correction, For hierarchical data, we introduce methods to construct valid conformal e-values, enabling control of the false discovery rate (FDR) through the e-BH procedure. In particular, we introduce and compare two approaches -- subsampling conformal e-values and hierarchical conformal e-values. Empirical results demonstrate that both approaches achieve valid FDR control while highlighting a tradeoff between stability and power. The subsampling-based method, though random, typically offers higher power, whereas the hierarchical approach, being deterministic, tends to be slightly less powerful. The effectiveness of the proposed methods is illustrated in two real-world applications.