Title: Inference-time Scaling for Time-series Processing
Primary area: learning on time series and dynamical systems
Keywords: Time-Series Forecasting; Time-Series Imputation; Bayesian Learning

Abstract: Scaling laws have fundamentally driven AI progress, particularly in large-scale models. However, as Web-scale pretraining data for such models nears saturation, focus increasingly shifts to new paradigms like inference-time scaling. While validated across various AI domains, its application to time-series tasks remains largely unexplored. This study addresses this gap by investigating whether inference-time scaling can be successfully adapted for time-series processing. First, multiple candidate outputs for a given input are generated based on a trained model. Second, motivated by the principle that better candidates reconstruct the observed data more accurately, we compute the reconstruction error for each candidate output. Third, these errors are used to determine weights of each candidate, and the final prediction is then formed as a weighted combination of the candidates. We present specific algorithmic instantiations of this new framework for two fundamental time-series tasks, namely forecasting and missing value imputation. Furthermore, we provide a theoretical analysis for the forecasting case to support the method's validity from a Bayesian uncertainty perspective. Extensive experimental evaluation across 7 benchmark datasets for both tasks convincingly verifies the effectiveness of our methodology: Incorporation of our methodology during the inference phase led to performance improvements in all 9 recent time-series methods. Source codes have been uploaded in the supplementary files.

TL;DR: This is the first study that investigates inference-time scaling for time-series forecasting and imputation, combining multiple candidate outputs via reconstruction-based weighting to achieve SOTA performance.