Part of International Conference on Representation Learning 2025 (ICLR 2025) Conference
Hao Wang, zhengnan li, Haoxuan Li, Xu Chen, Mingming Gong, BinChen, Zhichao Chen
Missing data imputation through distribution alignment has demonstrated advantages for non-temporal datasets but exhibits suboptimal performance in time-series applications. The primary obstacle is crafting a discrepancy measure that simultaneously (1) captures temporal patterns—accounting for periodicity and temporal dependencies inherent in time-series—and (2) accommodates non-stationarity, ensuring robustness amidst multiple coexisting temporal patterns. In response to these challenges, we introduce the Proximal Spectrum Wasserstein (PSW) discrepancy, a novel discrepancy tailored for comparing two \textit{sets} of time-series based on optimal transport. It incorporates a pairwise spectral distance to encapsulate temporal patterns, and a selective matching regularization to accommodate non-stationarity. Subsequently, we develop the PSW for Imputation (PSW-I) framework, which iteratively refines imputation results by minimizing the PSW discrepancy. Extensive experiments demonstrate that PSW-I effectively accommodates temporal patterns and non-stationarity, outperforming prevailing time-series imputation methods. Code is available at https://github.com/FMLYD/PSW-I.