# MD-split+: Practical Local Conformal Inference in High Dimensions

arXiv: https://arxiv.org/abs/2107.03280 · HTML: https://mlsanity.com/paper/2107.03280/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 17 references that are in the map.
- First posted on arXiv 7 Jul 2021.

## Builds on (most cited first, 6 of 6)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Nested conformal prediction and quantile out-of-bag ensemble methods](https://mlsanity.com/paper/1910.10562/) (2019)
- [CD-split and HPD-split: efficient conformal regions in high dimensions](https://mlsanity.com/paper/2007.12778/) (2020)
- [Converting High-Dimensional Regression to High-Dimensional Conditional Density Estimation](https://mlsanity.com/paper/1704.08095/) (2017)
- [Diagnostics for Conditional Density Models and Bayesian Inference Algorithms](https://mlsanity.com/paper/2102.10473/) (2021)
- [Conformal prediction with localization](https://mlsanity.com/paper/1908.08558/) (2019)

## Built on by (most cited first, 5 of 5)

- [Length Optimization in Conformal Prediction](https://mlsanity.com/paper/2406.18814/) (2024)
- [Conformal Prediction with Learned Features](https://mlsanity.com/paper/2404.17487/) (2024)
- [Few-Shot Calibration of Set Predictors via Meta-Learned Cross-Validation-Based Conformal Prediction](https://mlsanity.com/paper/2210.03067/) (2022)
- [Rectifying Conformity Scores for Better Conditional Coverage](https://mlsanity.com/paper/2502.16336/) (2025)
- [A Kernel-Based Conditional Two-Sample Test Using Nearest Neighbors (with Applications to Calibration, Regression Curves, and Simulation-Based Inference)](https://mlsanity.com/paper/2407.16550/) (2024)

## Abstract (arXiv)

Quantifying uncertainty in model predictions is a common goal for practitioners seeking more than just point predictions. One tool for uncertainty quantification that requires minimal assumptions is conformal inference, which can help create probabilistically valid prediction regions for black box models. Classical conformal prediction only provides marginal validity, whereas in many situations locally valid prediction regions are desirable. Deciding how best to partition the feature space X when applying localized conformal prediction is still an open question. We present MD-split+, a practical local conformal approach that creates X partitions based on localized model performance of conditional density estimation models. Our method handles complex real-world data settings where such models may be misspecified, and scales to high-dimensional inputs. We discuss how our local partitions philosophically align with expected behavior from an unattainable conditional conformal inference approach. We also empirically compare our method against other local conformal approaches.