# Confidence Intervals for Unobserved Events

arXiv: https://arxiv.org/abs/2211.03052 · HTML: https://mlsanity.com/paper/2211.03052/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 54 references that are in the map.
- First posted on arXiv 6 Nov 2022.

## Builds on (most cited first, 5 of 5)

- [Exact post-selection inference, with application to the lasso](https://mlsanity.com/paper/1311.6238/) (2013)
- [Exact Post-Selection Inference for Sequential Regression Procedures](https://mlsanity.com/paper/1401.3889/) (2014)
- [On the Impossibility of Learning the Missing Mass](https://mlsanity.com/paper/1503.03613/) (2015)
- [A Good-Turing estimator for feature allocation models](https://mlsanity.com/paper/1902.10490/) (2019)
- [Confidence Intervals for Selected Parameters](https://mlsanity.com/paper/1906.00505/) (2019)

## Abstract (arXiv)

Consider a finite sample from an unknown distribution over a countable alphabet. Unobserved events are alphabet symbols which do not appear in the sample. Estimating the probabilities of unobserved events is a basic problem in statistics and related fields, which was extensively studied in the context of point estimation. In this work we introduce a novel interval estimation scheme for unobserved events. Our proposed framework applies selective inference, as we construct confidence intervals (CIs) for the desired set of parameters. Interestingly, we show that obtained CIs are dimension-free, as they do not grow with the alphabet size. Further, we show that these CIs are (almost) tight, in the sense that they cannot be further improved without violating the prescribed coverage rate. We demonstrate the performance of our proposed scheme in synthetic and real-world experiments, showing a significant improvement over the alternatives. Finally, we apply our proposed scheme to large alphabet modeling. We introduce a novel simultaneous CI scheme for large alphabet distributions which outperforms currently known methods while maintaining the prescribed coverage rate.