# Local Prediction-Powered Inference

arXiv: https://arxiv.org/abs/2409.18321 · HTML: https://mlsanity.com/paper/2409.18321/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 30 references that are in the map.
- First posted on arXiv 26 Sep 2024.

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

- [Prediction-Powered Inference](https://mlsanity.com/paper/2301.09633/) (2023)
- [PPI++: Efficient Prediction-Powered Inference](https://mlsanity.com/paper/2311.01453/) (2023)
- [Semi-supervised Inference: General Theory and Estimation of Means](https://mlsanity.com/paper/1606.07268/) (2016)
- [Efficient and Adaptive Linear Regression in Semi-Supervised Settings](https://mlsanity.com/paper/1701.04889/) (2017)
- [Semi-Supervised Quantile Estimation: Robust and Efficient Inference in High Dimensional Settings](https://mlsanity.com/paper/2201.10208/) (2022)

## Built on by (most cited first, 8 of 8)

- [Prediction-Powered E-Values](https://mlsanity.com/paper/2502.04294/) (2025)
- [Calibeating Prediction-Powered Inference](https://mlsanity.com/paper/2604.21260/) (2026)
- [High-Dimensional Statistics: Reflections on Progress and Open Problems](https://mlsanity.com/paper/2605.05076/) (2026)
- [Do We Really Even Need Data? A Modern Look at Drawing Inference with Predicted Data](https://mlsanity.com/paper/2512.05456/) (2025)
- [Prediction-Powered Risk Monitoring of Deployed Models for Detecting Harmful Distribution Shifts](https://mlsanity.com/paper/2602.02229/) (2026)
- [Extending Prediction-Powered Inference through Conformal Prediction](https://mlsanity.com/paper/2510.16166/) (2025)
- [MEC: Machine-Learning-Assisted Generalized Entropy Calibration for Semi-Supervised Mean Estimation](https://mlsanity.com/paper/2604.05446/) (2026)
- [Conditional Evaluation of Language Models with Cheap Auxiliary Signals](https://mlsanity.com/paper/2608.16210/) (2026)

## Abstract (arXiv)

To infer a function value on a specific point x, it is essential to assign higher weights to the points closer to x, which is called local polynomial / multivariable regression. In many practical cases, a limited sample size may ruin this method, but such conditions can be improved by the Prediction-Powered Inference (PPI) technique. This paper introduced a specific algorithm for local multivariable regression using PPI, which can significantly reduce the variance of estimations without enlarge the error. The confidence intervals, bias correction, and coverage probabilities are analyzed and proved the correctness and superiority of our algorithm. Numerical simulation and real-data experiments are applied and show these conclusions. Another contribution compared to PPI is the theoretical computation efficiency and explainability by taking into account the dependency of the dependent variable.