Estimation of Structural Causal Model via Sparsely Mixing Independent Component Analysis
This work addresses inefficiencies in causal structure estimation for researchers in causal inference, though it is incremental as it builds on existing DAG models like LiNGAM.
The paper tackles the problem of inferring sparse causal structures from observational data by proposing a new estimation method for linear DAG models with non-Gaussian noises, which simultaneously estimates causal order and parameters and outperforms existing methods like LiNGAM and NOTEARS in numerical experiments.
We consider the problem of inferring the causal structure from observational data, especially when the structure is sparse. This type of problem is usually formulated as an inference of a directed acyclic graph (DAG) model. The linear non-Gaussian acyclic model (LiNGAM) is one of the most successful DAG models, and various estimation methods have been developed. However, existing methods are not efficient for some reasons: (i) the sparse structure is not always incorporated in causal order estimation, and (ii) the whole information of the data is not used in parameter estimation. To address {these issues}, we propose a new estimation method for a linear DAG model with non-Gaussian noises. The proposed method is based on the log-likelihood of independent component analysis (ICA) with two penalty terms related to the sparsity and the consistency condition. The proposed method enables us to estimate the causal order and the parameters simultaneously. For stable and efficient optimization, we propose some devices, such as a modified natural gradient. Numerical experiments show that the proposed method outperforms existing methods, including LiNGAM and NOTEARS.