backShift: Learning causal cyclic graphs from unknown shift interventions

TL;DR

backShift is a novel method for learning linear causal cyclic models with latent variables using equilibrium data from unknown shift interventions, relying solely on second moments and matrix diagonalization.

Contribution

It introduces a simple, second-moment-based approach for identifying causal cyclic graphs with latent variables under unknown interventions, with proven identifiability conditions.

Findings

Effective on simulated data

Successful application to flow cytometry data

Applicable to financial time series

Abstract

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.