Reframed GES with a Neural Conditional Dependence Measure

Xinwei Shen, Shengyu Zhu, Jiji Zhang, Shoubo Hu, Zhitang Chen

Research output: Chapter in book/report/conference proceedingConference proceedingpeer-review


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.
Original languageEnglish
Title of host publicationProceedings of the 38th Conference on Uncertainty in Artificial Intelligence, UAI 2022
EditorsJames Cussens, Kun Zhang
PublisherML Research Press
Number of pages10
ISBN (Print)9781713863298
Publication statusPublished - Aug 2022
Event38th Conference on Uncertainty in Artificial Intelligence, UAI 2022 - Eindhoven, Netherlands
Duration: 1 Aug 20225 Aug 2022 (Conference proceedings)

Publication series

NameProceedings of Machine Learning Research
ISSN (Print)2640-3498


Conference38th Conference on Uncertainty in Artificial Intelligence, UAI 2022
Internet address


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