High-dimensional causal discovery under non-Gaussianity
High-dimensional causal discovery under non-Gaussianity
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DOI：
10.1093/biomet/asz055
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发表时间：
2018-03
期刊：
影响因子：
2.7
通讯作者：
Y Samuel Wang;Mathias Drton
中科院分区：
文献类型：
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作者：
Y Samuel Wang;Mathias Drton
我们考虑基于线性结构方程递归系统的图形模型。这意味着存在变量的排序$\sigma$，使得每个观察变量$Y_v$是变量特定误差项和其他观察变量$Y_u$与$\sigma(U)<；\sigma(V)$的线性函数。因果关系，即线性函数依赖于哪些其他变量，可以使用有向图来描述。以前已经证明，当变量特定的误差项是非高斯时，可以从观测数据一致地估计确切的因果图，而不是马尔可夫等价类。我们提出了一种算法，在高维环境下也可以得到对图的一致估计，在高维环境中，变量的数量可能以比观测数量更快的速度增长，但在其中潜在的因果结构具有适当的稀疏性；具体地说，图的最大程度是受控制的。我们的理论分析是在对数凹误差分布的设置下进行的。
We consider graphical models based on a recursive system of linear structural equations. This implies that there is an ordering, $\sigma$, of the variables such that each observed variable $Y_v$ is a linear function of a variable-specific error term and the other observed variables $Y_u$ with $\sigma(u) < \sigma (v)$. The causal relationships, i.e., which other variables the linear functions depend on, can be described using a directed graph. It has previously been shown that when the variable-specific error terms are non-Gaussian, the exact causal graph, as opposed to a Markov equivalence class, can be consistently estimated from observational data. We propose an algorithm that yields consistent estimates of the graph also in high-dimensional settings in which the number of variables may grow at a faster rate than the number of observations, but in which the underlying causal structure features suitable sparsity; specifically, the maximum in-degree of the graph is controlled. Our theoretical analysis is couched in the setting of log-concave error distributions.