We consider causal structure estimation from time series data in which measurements are obtained at a coarser timescale than the causal timescale of the underlying system. Previous work has shown that such subsampling can lead to significant errors about the system's causal structure if not properly taken into account. In this paper, we first consider the search for system timescale causal structures that correspond to a given measurement timescale structure. We provide a constraint satisfaction procedure whose computational performance is several orders of magnitude better than previous approaches. We then consider finite-sample data as input, and propose the first constraint optimization approach for recovering system timescale causal structure. This algorithm optimally recovers from possible conflicts due to statistical errors. We then apply the method to real-world data, investigate the robustness and scalability of our method, consider further approaches to reduce underdetermination in the output, and perform an extensive comparison between different solvers on this inference problem. Overall, these advances build towards a full understanding of non-parametric estimation of system timescale causal structures from sub-sampled time series data.

中文翻译：

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从二次采样时间序列数据中发现因果关系的约束优化方法


我们考虑从时间序列数据进行因果结构估计，其中测量是在比底层系统的因果时间尺度更粗糙的时间尺度上获得的。先前的工作表明，如果没有适当考虑，这种子采样可能会导致系统因果结构出现重大错误。在本文中，我们首先考虑搜索与给定测量时间尺度结构相对应的系统时间尺度因果结构。我们提供了一种约束满足过程，其计算性能比以前的方法好几个数量级。然后，我们将有限样本数据视为输入，并提出第一个用于恢复系统时间尺度因果结构的约束优化方法。该算法可以最佳地从统计错误导致的可能冲突中恢复。然后，我们将该方法应用于现实世界的数据，研究我们方法的鲁棒性和可扩展性，考虑进一步减少输出中的不确定性的方法，并在这个推理问题上的不同求解器之间进行广泛的比较。总体而言，这些进步有助于充分理解子采样时间序列数据对系统时间尺度因果结构的非参数估计。