一种基于高阶累积量的因果结构学习算法

从观测数据中学习因果结构具有重要的应用价值。目前，一类学习因果结构的方法是基于函数因果模型假设，通过检验噪声与原因变量的独立性来学习因果结构。然而，该类方法涉及高计算复杂度的独立性检验过程，影响结构学习算法的实用性和鲁棒性。为此，提出了一种在线性非高斯模型下，利用高阶累积量作为独立性评估的因果结构学习算法。该算法主要分为两个步骤，第一个步骤是利用基于条件独立性约束的方法学习到因果结构的马尔可夫等价类，第二个步骤是定义了一种基于高阶累积量的得分，该得分可以判别两个随机变量的独立性，从而可以从马尔可夫等价类中搜索到最佳独立性得分的因果结构作为算法的输出。该算法的优势在于：a)相比基于核方法的独立性检验，该方法有较低的计算复杂度；b)基于得分搜索的方法，可以得到一个最匹配数据生成过程的模型，提高学习方法的鲁棒性。实验结果表明，基于高阶累积量的因果结构学习方法在合成数据中F₁得分提高了5%,并在真实数据中学习到更多的因果方向。

Higher-order cumulant-based algorithm for learning causal structure

Learning causal structure from observed data has important applications. An existing method for learning causal structure is to learn causal structure by testing the independence between noise and causal variables under the functional causal model assumption. However, such methods often involve highly computationally complex in process of testing independence, which affects the practicability and robustness of the structure learning algorithm. To this end, this paper proposed a causal structure learning algorithm that used higher-order cumulants as independence scores under a linear non-Gaussian model. The algorithm was mainly divided into two steps. The first step was to use the method based on conditional independence constraints to learn the Markov equivalence class of the causal structure. The second step was to define a score based on high-order cumulants, the score could determine the independence of two random variables so that the causal structure of the best independence score could be searched from the Markov equivalence class as the output of the algorithm. The advantages of this algorithm are: a) Compared with the independence test based on the kernel method, the method had lower computational complexity. b) The method based on score search could always obtain a model that best matches the data generation process, which improved the robustness of the learning method. Experimental results show that the high-order cumulant-based causal structure learning method improves the F1 score by 5% in synthetic data and learns more causal directions in real data.