Sparse Dynamic Distribution Decomposition: Efficient Integration of Trajectory and Snapshot Time Series Data

TL;DR

This paper introduces Sparse Dynamic Distribution Decomposition (Sparse DDD), a computationally efficient method that integrates trajectory and snapshot time series data by inferring sparse matrices over basis functions, improving analysis of biomedical data.

Contribution

The paper reformulates DDD to restrict to compact basis functions, leading to sparse matrices and reduced parameters, enabling efficient integration of different types of time series data.

Findings

Sparse DDD reduces computational complexity.

Effective integration of trajectory and snapshot data.

Applicable to biomedical population studies.

Abstract

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).