Provably Convergent Schrödinger Bridge with Applications to Probabilistic Time Series Imputation
This work addresses a theoretical gap in generative modeling for researchers, with incremental improvements in time series imputation applications.
The authors tackled the lack of convergence guarantees for the Schrödinger bridge algorithm with approximated projections, providing a first convergence analysis, and applied it to probabilistic time series imputation, achieving state-of-the-art results in healthcare and environmental data.
The Schrödinger 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 Schrödinger 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.