Smooth Flow Matching
This work addresses privacy and analysis issues in functional data for biomedical and health informatics, offering a practical solution where existing methods fall short, though it is incremental in building on flow-matching ideas.
The authors tackled the challenge of statistical analysis for functional data under privacy and sampling constraints by introducing Smooth Flow Matching (SFM), a generative framework that produces high-quality synthetic functional data, as demonstrated in simulations and an application to EHR data.
Functional data, i.e., smooth random functions observed over a continuous domain, are increasingly available in areas such as biomedical research, health informatics, and epidemiology. However, effective statistical analysis for functional data is often hindered by challenges such as privacy constraints, sparse and irregular sampling, infinite dimensionality, and non-Gaussian structures. To address these challenges, we introduce a novel framework named Smooth Flow Matching (SFM), tailored for generative modeling of functional data to enable statistical analysis without exposing sensitive real data. Built upon flow-matching ideas, SFM constructs a semiparametric copula flow to generate infinite-dimensional functional data, free from Gaussianity or low-rank assumptions. It is computationally efficient, handles irregular observations, and guarantees the smoothness of the generated functions, offering a practical and flexible solution in scenarios where existing deep generative methods are not applicable. Through extensive simulation studies, we demonstrate the advantages of SFM in terms of both synthetic data quality and computational efficiency. We then apply SFM to generate clinical trajectory data from the MIMIC-IV patient electronic health records (EHR) longitudinal database. Our analysis showcases the ability of SFM to produce high-quality surrogate data for downstream statistical tasks, highlighting its potential to boost the utility of EHR data for clinical applications.