# Shape-Adaptive Conditional Calibration for Conformal Prediction via Minimax Optimization

arXiv: https://arxiv.org/abs/2603.23374 · HTML: https://mlsanity.com/paper/2603.23374/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 56 references that are in the map.
- First posted on arXiv 24 Mar 2026.

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

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Theoretical Foundations of Conformal Prediction](https://mlsanity.com/paper/2411.11824/) (2024)
- [Minimum Volume Conformal Sets for Multivariate Regression](https://mlsanity.com/paper/2503.19068/) (2025)
- [Optimal Transport-based Conformal Prediction](https://mlsanity.com/paper/2501.18991/) (2025)
- [Optimal Model Selection for Conformalized Robust Optimization](https://mlsanity.com/paper/2507.04716/) (2025)

## Abstract (arXiv)

Achieving valid conditional coverage in conformal prediction is challenging due to the theoretical difficulty of satisfying pointwise constraints in finite samples. Building upon the characterization of conditional coverage through marginal moment restrictions, we introduce Minimax Optimization Predictive Inference (MOPI), a framework that generalizes prior work by optimizing over a flexible class of set-valued mappings during the calibration phase, rather than simply calibrating a fixed sublevel set. This minimax formulation effectively circumvents the structural constraints of predefined score functions, achieving superior shape adaptivity while maintaining a principled connection to the minimization of mean squared coverage error. Theoretically, we provide non-asymptotic oracle inequalities and show that the convergence rate of the coverage error attains the optimal order under regular conditions. The MOPI also enables valid inference conditional on sensitive attributes that are available during calibration but unobserved at test time. Empirical results on complex, non-standard conditional distributions demonstrate that MOPI produces more efficient prediction sets than existing baselines.