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.

该研究提出了一种名为 backShift 的方法，这种方法使用了特定类型的干预数据来学习具有潜在变量的线性因果循环模型，其性能在一些模拟数据以及在流式细胞术和金融时间序列应用中得到了验证。