# Conformal prediction with local weights: randomization enables local guarantees

arXiv: https://arxiv.org/abs/2310.07850 · HTML: https://mlsanity.com/paper/2310.07850/

## Key facts

- Cited by 48 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Oct 2023.

## Built on by (most cited first, 30 of 48)

- [Length Optimization in Conformal Prediction](https://mlsanity.com/paper/2406.18814/) (2024)
- [Conformal Prediction: A Data Perspective](https://mlsanity.com/paper/2410.06494/) (2024)
- [Conformal Prediction with Learned Features](https://mlsanity.com/paper/2404.17487/) (2024)
- [Evaluating the Utility of Conformal Prediction Sets for AI-Advised Image Labeling](https://mlsanity.com/paper/2401.08876/) (2024)
- [Synthetic-Powered Predictive Inference](https://mlsanity.com/paper/2505.13432/) (2025)
- [Conditional Conformal Risk Adaptation](https://mlsanity.com/paper/2504.07611/) (2025)
- [Improving the statistical efficiency of cross-conformal prediction](https://mlsanity.com/paper/2503.01495/) (2025)
- [ResCP: Reservoir Conformal Prediction for Time Series Forecasting](https://mlsanity.com/paper/2510.05060/) (2025)
- [Conditional Testing based on Localized Conformal p-values](https://mlsanity.com/paper/2409.16829/) (2024)
- [Conformal time series decomposition with component-wise exchangeability](https://mlsanity.com/paper/2406.16766/) (2024)
- [Conformal Calibration of Statistical Confidence Sets](https://mlsanity.com/paper/2411.19368/) (2024)
- [A note on conditional PAC-efficient reasoning in large language model routing](https://mlsanity.com/paper/2512.03057/) (2025)
- [Colorful Pinball: Density-Weighted Quantile Regression for Conditional Guarantee of Conformal Prediction](https://mlsanity.com/paper/2512.24139/) (2025)
- [Uncertainty Quantification With Multiple Sources](https://mlsanity.com/paper/2405.06479/) (2024)
- [Locally Adaptive Conformal Inference for Operator Models](https://mlsanity.com/paper/2507.20975/) (2025)
- [SpeedCP: Fast Kernel-based Conditional Conformal Prediction](https://mlsanity.com/paper/2509.24100/) (2025)
- [CLAPS: Aleatoric-Epistemic Scaling via Last-Layer Laplace for Conformal Regression](https://mlsanity.com/paper/2512.01384/) (2025)
- [Uncertainty Quantification and Data Efficiency in AI: An Information-Theoretic Perspective](https://mlsanity.com/paper/2512.05267/) (2025)
- [Co-optimization for Adaptive Conformal Prediction](https://mlsanity.com/paper/2603.01719/) (2026)
- [Conformal Prediction Assessment: A Framework for Conditional Coverage Evaluation and Selection](https://mlsanity.com/paper/2603.27189/) (2026)
- [Conformal Risk-Averse Decision Making with Action Conditional Guarantee](https://mlsanity.com/paper/2606.05551/) (2026)
- [Conformal Diffusion Models for Individual Treatment Effect Estimation and Inference](https://mlsanity.com/paper/2408.01582/) (2024)
- [Robust Bayesian Optimization via Localized Online Conformal Prediction](https://mlsanity.com/paper/2411.17387/) (2024)
- [Scalable and adaptive prediction bands with kernel sum-of-squares](https://mlsanity.com/paper/2505.21039/) (2025)
- [Individualised Counterfactual Examples Using Conformal Prediction Intervals](https://mlsanity.com/paper/2505.22326/) (2025)
- [Reliable Inference in Edge-Cloud Model Cascades via Conformal Alignment](https://mlsanity.com/paper/2510.17543/) (2025)
- [Conformalized Percentile Interval: Finite Sample Validity and Improved Conditional Performance](https://mlsanity.com/paper/2605.03233/) (2026)
- [Online Localized Conformal Prediction](https://mlsanity.com/paper/2605.05497/) (2026)
- [Budgeted Act-or-Defer Multi-Agent LLM Deliberation with Local Reliability Bounds](https://mlsanity.com/paper/2606.29654/) (2026)
- [Conformal Prediction for Uncertainty Estimation in Drug-Target Interaction Prediction](https://mlsanity.com/paper/2505.18890/) (2025)

## Abstract (arXiv)

In this work, we consider the problem of building distribution-free prediction intervals with finite-sample conditional coverage guarantees. Conformal prediction (CP) is an increasingly popular framework for building such intervals with distribution-free guarantees, but these guarantees only ensure marginal coverage: the probability of coverage is averaged over both the training and test data, meaning that there might be substantial undercoverage within certain subpopulations. Instead, ideally we would want to have local coverage guarantees that hold for each possible value of the test point's features. While the impossibility of achieving pointwise local coverage is well established in the literature, many variants of conformal prediction algorithm show favourable local coverage properties empirically. Relaxing the definition of local coverage can allow for a theoretical understanding of this empirical phenomenon. We propose randomly localized conformal prediction (RLCP), a method that builds on localized CP and weighted CP techniques to return prediction intervals that are not only marginally valid but also offer relaxed local coverage guarantees and validity under covariate shift. Through a series of simulations and real data experiments, we validate these coverage guarantees of RLCP while comparing it with the other local conformal prediction methods.