论文标题
稀疏动态分布分解：轨迹和快照时间序列数据的有效整合
Sparse Dynamic Distribution Decomposition: Efficient Integration of Trajectory and Snapshot Time Series Data
论文作者
论文摘要
动态分布分解（DDD）是在泰勒 - 金等人中引入的。 al。 （PLOS Comp Biol，2020）作为动态模式分解的变化。简而言之，通过在连续状态空间上使用基函数，DDD允许在这些基础函数上拟合连续的马尔可夫链，从而在分布之间连续映射。 DDD量表中的参数数量通过基函数数量的平方；我们重新制定了问题并限制了紧凑基函数的方法，这仅导致稀疏矩阵的推断，从而减少参数的数量。最后，我们演示了DDD如何适合整合两个轨迹时间序列（在后续时间点之间配对）和快照时间序列（未配对时间点）。能够整合这两种情况的方法与生物医学数据的分析特别相关，该方法研究在固定时间点（快照）和单个患者旅行中观察到人口，并具有反复的随访（轨迹）。
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).
