# On Training-Conditional Conformal Prediction and Binomial Proportion Confidence Intervals

arXiv: https://arxiv.org/abs/2502.07497 · HTML: https://mlsanity.com/paper/2502.07497/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 9 references that are in the map.
- First posted on arXiv 11 Feb 2025.

## Builds on (most cited first, 4 of 4)

- [Conformal Prediction: a Unified Review of Theory and New Challenges](https://mlsanity.com/paper/2005.07972/) (2020)
- [Verification of Neural Reachable Tubes via Scenario Optimization and Conformal Prediction](https://mlsanity.com/paper/2312.08604/) (2023)
- [Guarantees on Robot System Performance Using Stochastic Simulation Rollouts](https://mlsanity.com/paper/2309.10874/) (2023)
- [Reachability Analysis for Black-Box Dynamical Systems](https://mlsanity.com/paper/2410.07796/) (2024)

## Abstract (arXiv)

Estimating the expectation of a Bernoulli random variable based on N independent trials is a classical problem in statistics, typically addressed using Binomial Proportion Confidence Intervals (BPCI). In the control systems community, many critical tasks-such as certifying the statistical safety of dynamical systems-can be formulated as BPCI problems. Conformal Prediction (CP), a distribution-free technique for uncertainty quantification, has gained significant attention in recent years and has been applied to various control systems problems, particularly to address uncertainties in learned dynamics or controllers. A variant known as training-conditional CP was recently employed to tackle the problem of safety certification. In this note, we highlight that the use of training-conditional CP in this context does not provide valid safety guarantees. We demonstrate why CP is unsuitable for BPCI problems and argue that traditional BPCI methods are better suited for statistical safety certification.