Smooth Flow Matching for Synthesizing Functional Data

TL;DR

The paper introduces Smooth Flow Matching (SFM), a new generative framework for functional data that preserves privacy, handles irregular sampling, and produces smooth, high-quality synthetic functions for biomedical and health data analysis.

Contribution

SFM is a novel, flexible, and efficient generative model for functional data that does not rely on Gaussianity or low-rank assumptions, enabling privacy-preserving analysis.

Findings

SFM produces high-quality synthetic functional data in simulations.

SFM efficiently handles irregular and sparse observations.

Application to MIMIC-IV data demonstrates practical utility for clinical data synthesis.

Abstract

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 that enables statistical analysis without exposing sensitive real data. Under a copula framework, SFM constructs a parsimonious smooth flow to generate infinite-dimensional functional data, free of Gaussianity and 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 tasks, highlighting its potential to boost the utility of EHR data for clinical applications.