REGAIN: REconciliation GAIN-driven Auxiliary Direction Learning

Forecast reconciliation usually starts from a fixed measurement system and asks how forecasts should be projected onto a coherent space. We ask a different question: which additional linear measurements should be forecast and included in the reconciliation system? We propose REGAIN, a reconciliation-gain framework that learns normalized auxiliary directions, forecasts the induced series with a frozen forecasting oracle, and selects directions by their target-weighted loss reduction after augmented generalized least-squares reconciliation. Unlike variance-based components or predictability-based auxiliary selection, REGAIN optimizes the downstream effect of an auxiliary measurement on the final reconciled forecasts. We provide a statistical characterization showing that useful auxiliary directions must provide complementary information about unresolved target uncertainty, rather than merely being easy to forecast. The analysis also clarifies the covariance-risk reduction mechanism, the role of bias changes in realized quadratic risk, and the stability of estimated gain signals. A stagewise learning algorithm with held-out gain screening is developed, together with an optional joint refinement step. Experiments on Beijing PM2.5 and Australian Tourism data show that gain-selected measurements can improve both ordinary multivariate and hierarchical forecasts, especially when they reveal residual uncertainty not captured by the original measurement system.

Large Models Enabled Ubiquitous Wireless Sensing

In the era of 5G communication, the knowledge of channel state information (CSI) is crucial for enhancing network performance. This paper explores the utilization of language models for spatial CSI prediction within MIMO-OFDM systems. We begin by outlining the significance of accurate CSI in enabling advanced functionalities such as adaptive modulation. We review existing methodologies for CSI estimation, emphasizing the shift from traditional to data-driven approaches. Then a novel framework for spatial CSI prediction using realistic environment information is proposed, and experimental results demonstrate the effectiveness. This research paves way for innovative strategies in managing wireless networks.