# Prediction-powered inference for time series across space

arXiv: https://arxiv.org/abs/2610.08715 · HTML: https://mlsanity.com/paper/2610.08715/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 29 references that are in the map.
- First posted on arXiv 6 Oct 2026.

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

- [PPI++: Efficient Prediction-Powered Inference](https://mlsanity.com/paper/2311.01453/) (2023)
- [Prediction-Powered Inference with Imputed Covariates and Nonuniform Sampling](https://mlsanity.com/paper/2501.18577/) (2025)
- [Demystifying Prediction Powered Inference](https://mlsanity.com/paper/2601.20819/) (2026)
- [Spatially Robust Inference with Predicted and Missing at Random Labels](https://mlsanity.com/paper/2603.11368/) (2026)
- [Extending Prediction-Powered Inference through Conformal Prediction](https://mlsanity.com/paper/2510.16166/) (2025)

## Abstract (arXiv)

The following motif is common in spatiotemporal settings: we have a sequence of covariate and label pairs observed for a relatively short, recent time period. We have access to unlabeled covariates over a longer time period. Data is observed over many spatial locations. For instance, crop yield might be observed over a large geographical area for recent years, but weather data (which is informative about crop yield) is available for a much longer period. The goal is to estimate, at each spatial location, the expected label (e.g., crop yield) in the future and provide a valid confidence interval for this value. The observed time period alone is too short for reliable estimates. Imputing missing labels with machine learning can cause substantial bias. Prediction-powered inference (PPI) can correct for this bias, but it relies on an i.i.d. assumption that breaks under our expected temporal dependencies. Heteroskedasticity and autocorrelation consistent (HAC) procedures account for temporal correlation, but have not been adapted to cases where some labels are imputed. We provide reliable point estimates and confidence intervals given: short labeled time series (across spatial locations), a longer unlabeled time series, and an imperfect predictor of labels given covariates. We show our method outperforms natural alternatives.