Pairwise likelihood ratios for estimation of non-Gaussian structural equation models
Pairwise likelihood ratios for estimation of non-Gaussian structural equation models
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DOI：
10.5555/2567709.2502585
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发表时间：
2013-01
期刊：
影响因子：
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通讯作者：
Aapo Hyvärinen;Stephen M. Smith
中科院分区：
文献类型：
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作者：
Aapo Hyvärinen;Stephen M. Smith
我们提出了两个非高斯随机变量之间的因果方向，或效果方向的新措施。它们基于线性非高斯非循环模型（LiNGAM）下的似然比。我们还开发了简单的一阶近似的似然比，并分析它们的基础上相关的累积量为基础的措施，这可以证明找到正确的因果方向。我们展示了如何应用这些措施来估计LiNGAM两个以上的变量，甚至在更多的变量比观察的情况下。我们进一步扩展的方法，循环和非线性模型。该框架在统计上至少与现有的框架一样好，在数据点少或噪声数据的情况下，它是计算和概念上非常简单。模拟fMRI数据的结果表明，该方法可能是有用的神经成像的时间点的数量通常是相当小的。
We present new measures of the causal direction, or direction of effect, between two non-Gaussian random variables. They are based on the likelihood ratio under the linear non-Gaussian acyclic model (LiNGAM). We also develop simple first-order approximations of the likelihood ratio and analyze them based on related cumulant-based measures, which can be shown to find the correct causal directions. We show how to apply these measures to estimate LiNGAM for more than two variables, and even in the case of more variables than observations. We further extend the method to cyclic and nonlinear models. The proposed framework is statistically at least as good as existing ones in the cases of few data points or noisy data, and it is computationally and conceptually very simple. Results on simulated fMRI data indicate that the method may be useful in neuroimaging where the number of time points is typically quite small.