arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2201.09366cs.LGstat.ME
收藏

因果发现的最佳运输

Optimal transport for causal discovery

KTH Royal Institute of Technology(KTH皇家理工学院);Carnegie Mellon University(卡内基梅隆大学);Mohamed bin Zayed University of Artificial Intelligence(穆罕默德·本·扎耶德人工智能大学);Silo AI(Silo人工智能公司);Microsoft Research(微软研究院)

Ruibo Tu, Kun Zhang, Hedvig Kjellström, Cheng Zhang

摘要:

为了确定两个变量之间的因果关系,已经提出了基于功能因果模型(FCM)的方法,通过适当地限制模型类别;然而,性能对模型假设敏感,这使得它难以使用。在本文中,我们提供了一个新的动态系统的FCM视图,并提出了一个新的框架,确定因果方向的双变量的情况下。我们首先展示了FCM和最优运输之间的联系,然后研究了FCM约束下的最优运输。此外,通过利用FCM约束下的最优输运的动力学解释,我们确定了相应的静态因果对数据的潜在动力学过程。它提供了一个新的维度来描述静态的因果发现任务,同时享有更多的自由度来建模的定量因果影响。特别是,我们表明,加性噪声模型(ANMs)对应于体积保持无压流。因此,基于它们的速度场发散,我们引入了确定因果方向的准则。基于此准则,我们提出了一种新的基于最优传输的ANMs算法,该算法对模型的选择具有鲁棒性,并将其扩展到后非线性模型。我们的方法在合成和因果发现基准数据集上都展示了最先进的结果。

英文摘要:

To determine causal relationships between two variables, approaches based on Functional Causal Models (FCMs) have been proposed by properly restricting model classes; however, the performance is sensitive to the model assumptions, which makes it difficult to use. In this paper, we provide a novel dynamical-system view of FCMs and propose a new framework for identifying causal direction in the bivariate case. We first show the connection between FCMs and optimal transport, and then study optimal transport under the constraints of FCMs. Furthermore, by exploiting the dynamical interpretation of optimal transport under the FCM constraints, we determine the corresponding underlying dynamical process of the static cause-effect pair data. It provides a new dimension for describing static causal discovery tasks while enjoying more freedom for modeling the quantitative causal influences. In particular, we show that Additive Noise Models (ANMs) correspond to volume-preserving pressureless flows. Consequently, based on their velocity field divergence, we introduce a criterion for determining causal direction. With this criterion, we propose a novel optimal transport-based algorithm for ANMs which is robust to the choice of models and extend it to post-nonlinear models. Our method demonstrated state-of-the-art results on both synthetic and causal discovery benchmark datasets.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑