ICLR 2025

Published as a conference paper at ICLR 2025
OPTIMAL TRANSPORT FOR TIME-SERIES IMPUTATION
Hao Wang1
Zhengnan Li2
Haoxuan Li3
Xu Chen4
Mingming Gong5,6
Bin Chen7
Zhichao Chen1,∗
1Zhejiang University
2Communication University of China
3Peking University
4Renmin University of China
5The University of Melbourne
6Mohamed bin Zayed University of Artificial Intelligence
7University of Chinese Academy of Sciences
Ho-ward@outlook.com
fmlyd@cuc.edu.cn
justuschencse@zju.edu.cn
ABSTRACT
Missing data imputation through distribution alignment has demonstrated advan-
tages for non-temporal datasets but exhibits suboptimal performance in time-series
applications. The primary obstacle is crafting a discrepancy measure that simulta-
neously (1) captures temporal patterns—accounting for periodicity and temporal
dependencies inherent in time-series—and (2) accommodates non-stationarity, en-
suring 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 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 iter-
atively 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.
1
INTRODUCTION
The incompleteness of time-series data is a widespread issue in many fundamental fields. For example,
in healthcare (Prosperi et al., 2020), users utilize monitoring devices to track their health data, but
these records may be incomplete due to occasional device failures or disconnections. Similarly, in
manufacturing and...