ECRI: Evidence-based Interaction-Aware Time-Series Variable Selection

Time-series variable selection for multivariate forecasting must distinguish redundant variables from complementary ones while accounting for recurring variable costs. Selection rules that require each variable to provide an individual gain can miss jointly predictive variables, while predictive relevance alone does not determine whether a variable is worth acquiring. We propose Evidence-based Contextual Relevance Inference (ECRI), a framework that evaluates variable acquisition as a conditional, cost-aware joint decision. ECRI uses interaction features in a lightweight Bayesian surrogate and scores individual and joint acquisition actions by their conditional marginal evidence under separate variable and interaction costs. This permits a variable pair to satisfy the acquisition criterion without either variable first satisfying a single-variable criterion, while avoiding repeated training of downstream forecasting models. We characterize this mechanism under orthogonal-design conditions, explicitly accounting for the evidence and structural penalties of joint acquisition. The resulting variable-selection mask can be reused across forecasting backbones. Across three real-world sensor-network datasets and four forecasting backbones, ECRI removes 47.0–97.4% of optional variables and achieves the lowest prediction time and FLOPs among the six evaluated variable selectors, with competitive forecasting accuracy. These results support interaction-aware variable selection as a practical approach to reducing recurring forecasting computation.