# Reaching the Tail: Calibration Diversity Drives Conformal Coverage under Data Scarcity

arXiv: https://arxiv.org/abs/2608.21591 · HTML: https://mlsanity.com/paper/2608.21591/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 18 references that are in the map.
- First posted on arXiv 21 Aug 2026.

## Builds on (most cited first, 9 of 9)

- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [Conformal PID Control for Time Series Prediction](https://mlsanity.com/paper/2307.16895/) (2023)
- [Classifier Chains: A Review and Perspectives](https://mlsanity.com/paper/1912.13405/) (2019)
- [Conformal Prediction for Class-wise Coverage via Augmented Label Rank Calibration](https://mlsanity.com/paper/2406.06818/) (2024)
- [Predictive inference for time series: why is split conformal effective despite temporal dependence?](https://mlsanity.com/paper/2510.02471/) (2025)
- [Extreme Conformal Prediction: Reliable Intervals for High-Impact Events](https://mlsanity.com/paper/2505.08578/) (2025)

## Abstract (arXiv)

Multi-horizon rare-event forecasting is hard under long macroeconomic series' data constraints: labeled events are scarce, and standard uncertainty quantification assumes an exchangeability that autocorrelation violates. A controlled ablation shows an apparent rare-event threshold for Adaptive Conformal Inference instead reflects calibration-set size. Across 200 random calibration sets, support width of the nonconformity-score distribution explains up to 85% of coverage variance versus 2% for rare-event count; the same, not the same magnitude, replicates across synthetic conditions and five countries (five-country Spearman ρ 0.45-0.66 vs. 0.02-0.23). A diversity-maximizing selector built on this is the only strategy tested that improves long-horizon coverage (67.8% to 81.4% at six months); Mondrian, shift-robust, and extreme-value alternatives fail to close it. Mondrian even worsens coverage under oracle labels. A compact proposition explains why: coverage deficit reflects how closely the calibration set's upper quantile reaches the test distribution's. Diversity is necessary, not sufficient. Demonstrated on a two-stage U.S. recession-forecasting framework with RegressorChain, whether six-month coverage reaches 90% under honest scoring remains open, a question this paper quantifies rather than resolves.