Provably Convergent Schru00f6dinger Bridge with Applications to Probabilistic Time Series Imputation
Yu Chen,u00a0Wei Deng,u00a0Shikai Fang,u00a0Fengpei Li,u00a0Nicole Tianjiao Yang,u00a0Yikai Zhang,u00a0Kashif Rasul,u00a0Shandian Zhe,u00a0Anderson Schneider,u00a0Yuriy Nevmyvaka
The Schru00f6dinger bridge problem (SBP) is gaining increasing attention in generative modeling and showing promising potential even in comparison with the score-based generative models (SGMs). SBP can be interpreted as an entropy-regularized optimal transport problem, which conducts projections onto every other marginal alternatingly. However, in practice, only approximated projections are accessible and their convergence is not well understood. To fill this gap, we present a first convergence analysis of the Schru00f6dinger bridge algorithm based on approximated projections. As for its practical applications, we apply SBP to probabilistic time series imputation by generating missing values conditioned on observed data. We show that optimizing the transport cost improves the performance and the proposed algorithm achieves the state-of-the-art result in healthcare and environmental data while exhibiting the advantage of exploring both temporal and feature patterns in probabilistic time series imputation.
