Optimal Transport for Time Series Imputation
Keywords: Time series, Imputation
Abstract: 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) $\textit{captures temporal pattern}$—accounting for patterns such as periodicities and temporal dependencies inherent in time-series—and (2) $\textit{accommodates non-stationarity}$, ensuring robustness amidst multiple coexisting temporal patterns. In response to these challenges, we introduce the Proximal Spectrum Wasserstein (PSW) discrepancy based on the stochastic optimal transport framework, which incorporates a pairwise spectral distance to encapsulate temporal patterns, coupled with selective matching regularization to accommodate non-stationarity. Building upon PSW, 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 addresses these challenges and significantly outperforms prevailing time-series imputation methods.
Primary Area: applications to computer vision, audio, language, and other modalities
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Submission Number: 14099
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