The Schr\"odinger 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 Schr\"odinger 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.

翻译：薛定谔桥问题（SBP）在生成建模领域日益受到关注，甚至在与基于分数的生成模型（SGMs）相比时也展现出巨大潜力。SBP可被解释为一种熵正则化的最优传输问题，其通过交替向每个边际分布进行投影来完成优化。然而在实际应用中，仅能获得近似投影，且其收敛性尚未得到充分理解。为弥补这一空白，我们首次提出了基于近似投影的薛定谔桥算法的收敛性分析。在实际应用方面，我们将SBP应用于概率时间序列插补，通过生成以观测数据为条件的缺失值。研究表明，优化传输成本可提升模型性能，所提出的算法在医疗健康与环境数据上达到了最先进水平，同时展现了在概率时间序列插补中同时挖掘时间模式与特征模式的优势。