Sparse Dynamic Distribution Decomposition: Efficient Integration of Trajectory and Snapshot Time Series Data
This work addresses the need for methods to integrate paired and unpaired time series data in biomedical studies, though it is incremental as it builds on an existing DDD framework.
The authors tackled the problem of high parameter scaling in Dynamic Distribution Decomposition (DDD) by reformulating it with compact basis functions to infer sparse matrices, reducing parameters, and demonstrated its ability to integrate both trajectory and snapshot time series data, with applications in biomedical analysis.
Dynamic Distribution Decomposition (DDD) was introduced in Taylor-King et. al. (PLOS Comp Biol, 2020) as a variation on Dynamic Mode Decomposition. In brief, by using basis functions over a continuous state space, DDD allows for the fitting of continuous-time Markov chains over these basis functions and as a result continuously maps between distributions. The number of parameters in DDD scales by the square of the number of basis functions; we reformulate the problem and restrict the method to compact basis functions which leads to the inference of sparse matrices only -- hence reducing the number of parameters. Finally, we demonstrate how DDD is suitable to integrate both trajectory time series (paired between subsequent time points) and snapshot time series (unpaired time points). Methods capable of integrating both scenarios are particularly relevant for the analysis of biomedical data, whereby studies observe population at fixed time points (snapshots) and individual patient journeys with repeated follow ups (trajectories).