Prediction-powered inference for time series across space

Shahzar Rizvi; David Burt; Vishwak Srinivasan; Renato Berlinghieri; Stefano Del Col; Tamara Broderick

stat.MEOct 6, 2026

Prediction-powered inference for time series across space

Authors: Shahzar Rizvi, David Burt, Vishwak Srinivasan, Renato Berlinghieri, Stefano Del Col, Tamara Broderick

Organizations: MIT LIDS · UMass Amherst · Stanford University · Assicurazioni Generali

Abstract

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.

Figures & tables

	$\Delta$	$\mathbb{E}[\hat{\Delta}]$	$\mathbb{E}[\hat{\theta}^{\rm PPI}-\theta]$
Chunking	$-0.606$	$-0.602$	$0.003$
Interleaving	$-0.080$	$-0.001$	$0.078$

Table 1: For each row (using a chunked or interleaved split), we report true prediction bias (left column), estimated prediction bias (middle), and bias of the PPI estimate (right). In each column, we report the expected result by averaging over

10^{5}

replicates. In every case, the standard error has size strictly less than

3\times 10^{-3}

; see Table 3 in Appendix C for the full standard errors.

	Less Extreme Weather			More Extreme Weather
Method	Scaled RMSE	Coverage	Scaled Half-Width	Scaled RMSE	Coverage	Scaled Half-Width
Classical	$0.0503$	$30.02\%$	$0.0194$	$0.0372$	$31.56\%$	$0.0147$
IWI	$0.0399$	$21.19\%$	$0.0088$	$0.0302$	$20.79\%$	$0.0064$
chunkPPI	$0.0299$	$30.91\%$	$0.0115$	$0.0218$	$32.88\%$	$0.0087$
HAC	$0.0503$	$91.72\%$	$0.0871$	$0.0372$	$88.00\%$	$0.0593$
PPITSAS (ours)	$0.0299$	$93.45\%$	$0.0527$	$0.0218$	$92.64\%$	$0.0362$

Table 2: For each method, we report the performance metrics in the less extreme weather setting (left) and the more extreme weather setting (right). The best performance for each metric, according to the goalposts defined in Section 5.1 , are shaded in green; in the event of a tie, all winners are shaded. We ignore scaled half-widths for coverages below 85%, and shade them in gray.

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

\mathcal{D}_{\rm L}=\big\{(X_{t}(s^{\prime}),Y_{t}(s^{\prime}))\big\}_{t\in\mathcal{T}_{\rm L},\,s^{\prime}\in\mathcal{S}}

Appendix

Algorithm 1

\mathsf{PPITSAS}

. PPI for time-series across space

\bar{W}\leftarrow\frac{1}{T}\sum_{t=1}^{T}W_{t}.

(13)

Appendix

Algorithm 2

\mathsf{HAC}

. Heteroskedasticity and autocorrelation consistent variance estimation [ 14 ]

	${\rm E}[\Delta]$	${\rm E}[\hat{\Delta}]$	${\rm E}[\hat{\theta}^{\rm PPI}-\theta]$
Chunking	$-0.6058\;(0.0020)$	$-0.6024\;(0.0022)$	$-0.0029\;(0.0011)$
Interleaving	$-0.0796\;(0.0008)$	$-0.0012\;(0.0002)$	$-0.0778\;(0.0007)$

Appendix

Table 3: For each row (using a chunked or interleaved split of the labeled data), we report the true prediction bias (left column), estimated prediction bias (middle column), and bias of the PPI estimate (right column). In each column, we report the result averaged over

10^{5}

replicates. Monte Carlo standard errors are reported in parentheses.

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Prediction-Powered Inference Across Many Tasks for AI Evaluation & Social Science Research

Nicolas Emmenegger, Ellery Stahler, Chara Podimata

MIT Cambridge, MA

Artificial Intelligence Evaluation Survey Computational Social Science Recalibration Ground Truth

Open paper AskPDF arXiv

Many applications require statistically valid inference across many related tasks, while using only a handful of high-quality labels per hypothesis. In AI evaluation, these tasks may correspond to model behaviors across prompts, subgroups, or hypotheses; in social science surveys, they may correspond to related questions, populations, or measurement conditions. Prediction-powered inference (PPI) uses abundant but inexpensive proxy measurements to improve inference from limited, ground-truth labels, but commonly used methods treat tasks independently and therefore fail to exploit shared structure across related tasks. This limitation is especially important in settings where only a small number of labels are available per task. To address this issue, we introduce a multi-task prediction-powered inference framework that uses labeled data from related tasks to improve power while preserving task-specific inference. Our methods exploit the shared structure in the proxy-ground-truth relationship through cross-task recalibration, while retaining within-task rectification and power tuning to construct accurate point estimates and confidence intervals. We prove that efficiency gains beyond power-tuned PPI are only possible when the proxy-ground-truth relationship contains nonlinear structure; affine cross-task recalibrations are asymptotically equivalent to using the original proxy. We complement our theoretical findings with experiments on synthetic and semi-synthetic datasets, as well as a case study auditing language models on election-related information during the 2024 U.S. presidential election. Using a large human-annotation study, we show that cross-task recalibration can substantially reduce confidence interval widths when labels are scarce.

Abstract

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