RI: Small: Collaborative Research: Learning Causal Structure from Complex Time Series Data

在许多重要的领域，人们必须了解动态系统的因果结构，以便设计适当的干预措施、政策和实验。当科学家不能足够快地测量系统和/或忽略因果关系重要变量时，该项目为这种学习开发了一个有充分根据的理论和实用算法。此外，理论和算法将集中在最具挑战性的情况下，当科学家不知道由于缺乏速度或广度而丢失了多少信息时。例如，认知神经科学实验中的功能磁共振成像（fMRI）测量大约每两秒钟进行一次，但神经区域之间的交流要快得多（尽管具体快多少还不得而知）。此外，神经科学家几乎肯定无法记录所有有因果关系的重要变量，比如其他身体状态。同样，许多气候学研究忽略了重要的变量（如土地利用），并且只得出每月（或较慢）的测量结果，尽管潜在的现象可能是在更快的时间尺度上进行的。该项目将首先关注从欠采样时间序列（具有未知的欠采样率）中学习的挑战，这将需要(a)扩展因果图模型的正式框架以表示这种可能性；(b)提供一组描述欠采样下因果结构变化的定理；(c)开发算法，从从欠采样数据中学习到的因果结构中推断出“真实”时间尺度因果结构的约束；(d)在预先存在的、开源的因果学习环境中实现这些算法；(e)通过广泛的模拟在计算机上测试这些算法；(f)将它们应用于现实世界的数据集，包括大规模的神经成像数据。最后一步尤其重要，因为它将使早期开发的理论和算法能够在现实世界中得到验证。与此同时，该项目将解决同样的六个挑战，即数据采样正确，但缺少因果关系显著的变量。最后，这两部分将合并为一个集成的框架和算法，以应对这两种挑战同时出现的情况。由此产生的定理、算法和应用集将扩展当前的因果建模和因果结构学习理论，并解决研究人员从复杂的、现实世界的时间序列数据中进行因果学习的实际需求。

In many important domains, one must learn the causal structure of a dynamical system in order to design appropriate interventions, policies, and experiments. This project develops a well founded theory and practical algorithms for such learning when scientists cannot measure the system quickly enough and/or omit causally important variables. Moreover, the theory and algorithms will focus on the most challenging case, when scientists do not know how much information is missing because of lack of either speed or breadth. For example, fMRI measurements in cognitive neuroscience experiments occur roughly every two seconds, but communication between neural regions happens much more quickly (though exactly how much more quickly is unknown). In addition, neuroscientists are almost certainly unable to record all causally significant variables, such as other bodily states. Similarly, many climatological studies omit important variables (e.g., land use) and yield only monthly (or slower) measurements, even though the underlying phenomena presumably proceed on a faster timescale.This project will first focus on the challenge of learning from an undersampled time series (with unknown undersample rate), which will require (a) extending the formal framework of causal graphical models to represent such possibilities; (b) providing a set of theorems characterizing how causal structures change under undersampling; (c) developing algorithms that infer constraints on the "true" timescale causal structure from the causal structure learned from the undersampled data; (d) implementing these algorithms in a pre-existing, open-source causal learning environment; (e) testing these algorithms in silico through extensive simulations; and (f) applying them to real world datasets, including large-scale neuroimaging data. This last step is particularly important as it will enable real-world validation of the theory and algorithms developed earlier. In parallel, the project will address the same six challenges for situations in which data are correctly sampled, but causally significant variables are missing. Finally, these two pieces will be merged into an integrated framework and algorithms for situations in which both challenges arise simultaneously. The resulting set of theorems, algorithms, and applications will both extend the current theory of causal modeling and causal structure learning, and also address the practical needs of researchers engaged in causal learning from complex, real-world time series data.