Sparse estimation of Linear Non-Gaussian Acyclic Model for Causal Discovery
Sparse estimation of Linear Non-Gaussian Acyclic Model for Causal Discovery
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DOI：
10.1016/j.neucom.2021.06.083
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发表时间：
2021-10
期刊：
影响因子：
6
通讯作者：
Kazuharu Harada;H. Fujisawa
中科院分区：
文献类型：
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作者：
Kazuharu Harada;H. Fujisawa
我们考虑从观测数据推断因果结构的问题，特别是当结构稀疏时。这种类型的问题通常被公式化为有向无环图（DAG）模型的推理。线性非高斯无环模型（LiNGAM）是最成功的DAG模型之一，各种估计方法已经发展。然而，现有的方法是不有效的，由于一些原因：（i）稀疏结构并不总是被纳入因果顺序估计，（ii）高阶矩的信息的数据没有被用于参数估计。为了解决这些问题，我们提出了一种新的估计方法的线性DAG模型与非高斯噪声。该方法是基于一个单一的统计准则，其中包括独立分量分析（伊卡）和两个惩罚条款的对数似然。这两个惩罚分别与稀疏性和一致性条件有关。该准则使我们能够在整个估计过程中利用稀疏结构和高阶矩的信息。为了稳定和有效的优化，我们提出了一些设备，如修改的自然梯度。数值实验表明，该方法优于现有的方法。
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 information of higher-order moments 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 a single statistical criterion that includes the log-likelihood of independent component analysis (ICA) and two penalty terms. The two penalties are related to the sparsity and the consistency condition, respectively. This criterion enables us to leverage the sparse structure and the information of higher-order moments throughout the estimation. For stable and efficient optimization, we propose some devices, such as a modified natural gradient. Numerical experiments show that the proposed method outperforms the existing methods.