DirectLiNGAM: A Direct Method for Learning a Linear Non-Gaussian Structural Equation Model
DirectLiNGAM: A Direct Method for Learning a Linear Non-Gaussian Structural Equation Model
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DOI：
10.5555/1953048.2021040
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发表时间：
2011-01
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通讯作者：
Shohei Shimizu;Takanori Inazumi;Yasuhiro Sogawa;Aapo Hyvärinen;Y. Kawahara;T. Washio;P. Hoyer;K. Bollen
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文献类型：
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作者：
Shohei Shimizu;Takanori Inazumi;Yasuhiro Sogawa;Aapo Hyvärinen;Y. Kawahara;T. Washio;P. Hoyer;K. Bollen
结构方程模型和贝叶斯网络已被广泛用于分析连续变量之间的因果关系。在这种框架中，线性非循环模型通常用于对变量的数据生成过程进行建模。最近，它表明，使用非高斯识别的完整结构的线性非循环模型，即，因果排序的变量和它们的连接强度，而不使用任何先验知识的网络结构，这是不是与传统的方法的情况下。然而，现有的估计方法基于迭代搜索算法，并且可能不会在有限数量的步骤中收敛到正确的解。在本文中，我们提出了一个新的直接方法来估计因果排序和连接强度的基础上非高斯。与以前的方法相比，我们的算法不需要算法参数，并保证收敛到正确的解决方案在一个小的固定的步骤数，如果数据严格遵循的模型，也就是说，如果所有的模型假设都得到满足，样本量是无限的。
Structural equation models and Bayesian networks have been widely used to analyze causal relations between continuous variables. In such frameworks, linear acyclic models are typically used to model the data-generating process of variables. Recently, it was shown that use of non-Gaussianity identifies the full structure of a linear acyclic model, that is, a causal ordering of variables and their connection strengths, without using any prior knowledge on the network structure, which is not the case with conventional methods. However, existing estimation methods are based on iterative search algorithms and may not converge to a correct solution in a finite number of steps. In this paper, we propose a new direct method to estimate a causal ordering and connection strengths based on non-Gaussianity. In contrast to the previous methods, our algorithm requires no algorithmic parameters and is guaranteed to converge to the right solution within a small fixed number of steps if the data strictly follows the model, that is, if all the model assumptions are met and the sample size is infinite.