In a nonparametric setting, the causal structure is often identifiable only up to Markov equivalence, and for the purpose of causal inference, it is useful to learn a graphical representation of the Markov equivalence class (MEC). In this paper, we revisit the Greedy Equivalence Search (GES) algorithm, which is widely cited as a score-based algorithm for learning the MEC of the underlying causal structure. We observe that in order to make the GES algorithm consistent in a nonparametric setting, it is not necessary to design a scoring metric that evaluates graphs. Instead, it suffices to plug in a consistent estimator of a measure of conditional dependence to guide the search. We therefore present a reframing of the GES algorithm, which is more flexible than the standard score-based version and readily lends itself to the nonparametric setting with a general measure of conditional dependence. In addition, we propose a neural conditional dependence (NCD) measure, which utilizes the expressive power of deep neural networks to characterize conditional independence in a nonparametric manner. We establish the optimality of the reframed GES algorithm under standard assumptions and the consistency of using our NCD estimator to decide conditional independence. Together these results justify the proposed approach. Experimental results demonstrate the effectiveness of our method in causal discovery, as well as the advantages of using our NCD measure over kernel-based measures.
翻译:在非对称环境下,因果关系结构往往只可确定到Markov等同,而且为了因果关系推断的目的,有必要了解Markov等同类(MEC)的图形表示方式。在本文中,我们重新审视了贪婪等同搜索算法(GES),该算法被广泛引用为一种基于分数的算法,用于学习基本因果关系结构的MEC。我们注意到,为使GES算法在非对称环境中保持一致,没有必要设计一个评分标准,用以评价图表。相反,我们只需用一致的衡量标准依赖度衡量标准等同类(MEC),就足以填补对有条件依赖度的衡量尺度。因此,我们提出重整GES算法(GES算法)比标准的得分数版本更为灵活,并很容易以一般的有条件依赖度标准衡量标准,适用于非对等同性设定的非对等值。此外,我们提议采用以内深神经基网络的明显能力来描述有条件的独立特征。我们用ARC模型的优化性衡量方法来确定我们共同确定标准性结果的正确性。