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

在许多重要领域，人们必须了解动力系统的因果结构，以便设计适当的干预、政策和实验。当科学家不能足够快地测量系统和/或省略因果重要变量时，这个项目为这种学习开发了一个有充分基础的理论和实用算法。此外，理论和算法将专注于最具挑战性的情况，即科学家不知道由于速度或广度不足而丢失了多少信息。例如，认知神经科学实验中的fMRI测量大约每两秒进行一次，但神经区域之间的交流要快得多(尽管确切地说快了多少还不得而知)。此外，神经学家几乎肯定无法记录所有具有因果意义的变量，例如其他身体状态。同样，许多气候学研究忽略了重要的变量(例如，土地利用)，只产生每月(或更慢)的测量，即使潜在的现象可能在更快的时间尺度上进行。这个项目将首先关注从欠采样时间序列(具有未知的欠采样速率)中学习的挑战，这将需要(A)扩展因果图形模型的形式框架以表示这种可能性；(B)提供一组定理来描述在欠采样下因果结构如何变化；(C)开发算法，从从欠采样数据学习的因果结构中推断对“真实的”时间尺度因果结构的约束；(D)在预先存在的开放源码因果学习环境中实施这些算法；(E)通过广泛的模拟在Silico中测试这些算法；以及(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。这最后一步特别重要，因为它将使先前开发的理论和算法能够在现实世界中得到验证。同时，该项目将解决同样的六个挑战，即数据抽样正确，但因果关系重大的变量缺失。最后，这两个部分将合并为一个综合框架和算法，以应对这两个挑战同时出现的情况。所得到的一组定理、算法和应用将扩展当前的因果建模和因果结构学习的理论，并解决从事从复杂的真实世界时间序列数据进行因果学习的研究人员的实际需求。

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.