Is Precise Recovery Necessary? A Task-Oriented Imputation Approach for Time Series Forecasting on Variable Subset

Variable Subset Forecasting (VSF) refers to a unique scenario in multivariate time series forecasting, where available variables in the inference phase are only a subset of the variables in the training phase. VSF presents significant challenges as the entire time series may be missing, and neither inter- nor intra-variable correlations persist. Such conditions impede the effectiveness of traditional imputation methods, primarily focusing on filling in individual missing data points. Inspired by the principle of feature engineering that not all variables contribute positively to forecasting, we propose <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><b>T</b></u>ask-<underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><b>O</b></u>riented <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><b>I</b></u>mputation for <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><b>VSF</b></u> (TOI-VSF), a novel framework shifts the focus from accurate data recovery to directly support the downstream forecasting task. TOI-VSF incorporates a self-supervised imputation module, agnostic to the forecasting model, designed to fill in missing variables while preserving the vital characteristics and temporal patterns of time series data. Additionally, we implement a joint learning strategy for imputation and forecasting, ensuring that the imputation process is directly aligned with and beneficial to the forecasting objective. Extensive experiments across four datasets demonstrate the superiority of TOI-VSF, outperforming baseline methods by 15% on average.