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We consider the problem of inferring the causal structure from observationaldata, especially when the structure is sparse. This type of problem is usuallyformulated as an inference of a directed acyclic graph (DAG) model. The linearnon-Gaussian acyclic model (LiNGAM) is one of the most successful DAG models,and various estimation methods have been developed. However, existing methodsare not efficient for some reasons: (i) the sparse structure is not alwaysincorporated in causal order estimation, and (ii) the whole information of thedata is not used in parameter estimation. To address {these issues}, we proposea new estimation method for a linear DAG model with non-Gaussian noises. Theproposed method is based on the log-likelihood of independent componentanalysis (ICA) with two penalty terms related to the sparsity and theconsistency condition. The proposed method enables us to estimate the causalorder and the parameters simultaneously. For stable and efficient optimization,we propose some devices, such as a modified natural gradient. Numericalexperiments show that the proposed method outperforms existing methods,including LiNGAM and NOTEARS.

Estimation of Structural Causal Model via Sparsely Mixing Independent Component Analysis