基于谱结构学习，从不规则临床时间序列中挖掘变量间因果关系。
Spectral structure learning for clinical time series
- 用结构高斯过程建模多患者不规则时间序列，通过可微无环约束优化图结构。
- 在20个任务、平均度数3时，边恢复中位召回率达93%，精确率71%。
- 适合医疗数据建模者，尤其关注时间序列依赖关系挖掘的临床研究者。
我们开发并评估了一种用于临床时间序列的结构学习算法。临床时间序列是多患者观测的多变量、不规则采样时间序列，对现有结构学习算法构成挑战。我们假设时间序列是结构高斯过程（StructGP）的实现，即一个k维多输出或多任务平稳高斯过程（GP），不同患者共享相同的协方差函数。StructGP编码了时间序列间的有序条件依赖关系，以有向无环图表示。我们实现了改进的NOTEARS算法，该算法基于可微的无环性定义，通过求解一系列连续优化问题来恢复图结构。模拟结果表明，在平均度数3、20个任务条件下，边恢复的中位召回率为0.93%（四分位距0.86–0.97），中位精确率为0.71%（0.57–0.84）。我们进一步表明，正则化路径对于正确识别图结构至关重要。通过StructGP，我们提出了一种灵活适应不同时间序列规律性的依赖模型，同时能从观测数据中学习这些依赖关系。
原文摘要 · Abstract (English)
We develop and evaluate a structure learning algorithm for clinical time series. Clinical time series are multivariate time series observed in multiple patients and irregularly sampled, challenging existing structure learning algorithms. We assume that our times series are realizations of StructGP, a k-dimensional multi-output or multi-task stationary Gaussian process (GP), with independent patients sharing the same covariance function. StructGP encodes ordered conditional relations between time series, represented in a directed acyclic graph. We implement an adapted NOTEARS algorithm, which based on a differentiable definition of acyclicity, recovers the graph by solving a series of continuous optimization problems. Simulation results show that up to mean degree 3 and 20 tasks, we reach a median recall of 0.93% [IQR, 0.86, 0.97] while keeping a median precision of 0.71% [0.57-0.84], for recovering directed edges. We further show that the regularization path is key to identifying the graph. With StructGP, we proposed a model of time series dependencies, that flexibly adapt to different time series regularity, while enabling us to learn these dependencies from observations.
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