backShift：从未知移位干预中学习因果循环图
backShift: Learning causal cyclic graphs from unknown shift interventions
摘要：
我们提出了一个简单的方法来学习线性因果循环模型的潜变量的存在。该方法依赖于在特定类型的干预（“转移干预”）下记录的模型的平衡数据。这些干预措施的地点和力度不必知道，可以从数据中估计出来。我们的方法，称为backShift，只使用数据的二阶矩，并执行简单的联合矩阵对角化，适用于协方差阵之间的差异。我们给出了系统可识别性的一个充分必要条件，在一些相当一般的假设下，当且仅当至少有三个不同的实验设置，其中一个可以是纯观测数据，这是几乎肯定满足。我们展示了一些模拟数据的性能和应用在流式细胞术和金融时间序列。该代码作为R-package backShift提供。
英文摘要：
We propose a simple method to learn linear causal cyclic models in the presence of latent variables. The method relies on equilibrium data of the model recorded under a specific kind of interventions ("shift interventions"). The location and strength of these interventions do not have to be known and can be estimated from the data. Our method, called backShift, only uses second moments of the data and performs simple joint matrix diagonalization, applied to differences between covariance matrices. We give a sufficient and necessary condition for identifiability of the system, which is fulfilled almost surely under some quite general assumptions if and only if there are at least three distinct experimental settings, one of which can be pure observational data. We demonstrate the performance on some simulated data and applications in flow cytometry and financial time series. The code is made available as R-package backShift.
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