Keywords: Interventions, causal inference, causally insufficient systems, linear SEMs.
TL;DR: We propose a scalable algorithm that recovers intervention targets in linear structural equation models in the presence of latent variables.
Abstract: This paper considers the problem of estimating unknown intervention targets in causal directed acyclic graphs from observational and interventional data in the presence of latent variables. The focus is on linear structural equation models with soft interventions. The existing approaches to this problem involve extensive conditional independence tests, and they estimate the unknown intervention targets alongside learning the structure of the causal model in its entirety. This joint learning approach to estimating the intervention targets results in algorithms that are not scalable as graph sizes grow. This paper proposes an approach that does not necessitate learning the entire causal model and focuses on learning only the intervention targets. The key idea of this approach is the property that interventions impose sparse changes in the precision matrix of a linear model. Leveraging this property, the proposed framework consists of a sequence of precision difference estimation steps. Furthermore, the necessary knowledge to refine an observational Markov equivalence class (MEC) to an interventional MEC is inferred. Simulation results are provided to illustrate the scalability of the proposed algorithm and compare it with those of the existing approaches.
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