arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2210.06201cs.LGcs.AI
收藏

通过拓扑排序进行因果发现的扩散模型

Diffusion Models for Causal Discovery via Topological Ordering

The University of Edinburgh(爱丁堡大学);Canon Medical Research Europe(佳能医疗欧洲研究院);The Alan Turing Institute(艾伦·图灵研究所)

Pedro Sanchez, Xiao Liu, Alison Q O'Neil, Sotirios A. Tsaftaris

AI总结:

提出DiffAN算法,利用扩散概率模型学习Hessian函数实现因果图的拓扑排序,支持无需重训更新Hessian并用样本子集近似计算,在高达500节点和10^5样本的大规模数据集上扩展性优异且小数据集上表现媲美SOTA。

摘要:

在附加假设(如将函数关系约束为带加性噪声的非线性模型(ANM))下,从观测数据中发现因果关系成为可能。即使有强假设,因果发现仍涉及在有向无环图(DAGs)空间上的昂贵搜索问题。拓扑排序方法通过在排列空间而非图空间上搜索,减少了因果发现的优化空间。对于ANM,数据对数似然的Hessian矩阵可用于寻找因果图中的叶节点,从而实现其拓扑排序。然而,随着变量数和样本数增加,现有计算Hessian的方法仍无法有效扩展。因此,受扩散概率模型(DPMs)近期创新的启发,我们提出了DiffAN,这是一种利用DPMs学习Hessian函数的拓扑排序算法。我们提出了无需重新训练神经网络即可更新所学Hessian的理论,并证明使用样本子集计算可给出排序的准确近似,从而允许扩展到具有更多样本和变量的数据集。我们实证表明,该方法在节点数高达500、样本数高达10^5的数据集上扩展性极佳,同时在小型数据集上与最先进的因果发现方法表现相当。

英文摘要:

Discovering causal relations from observational data becomes possible with additional assumptions such as considering the functional relations to be constrained as nonlinear with additive noise (ANM). Even with strong assumptions, causal discovery involves an expensive search problem over the space of directed acyclic graphs (DAGs). \emph{Topological ordering} approaches reduce the optimisation space of causal discovery by searching over a permutation rather than graph space. For ANMs, the \emph{Hessian} of the data log-likelihood can be used for finding leaf nodes in a causal graph, allowing its topological ordering. However, existing computational methods for obtaining the Hessian still do not scale as the number of variables and the number of samples increase. Therefore, inspired by recent innovations in diffusion probabilistic models (DPMs), we propose \emph{DiffAN}\footnote{Implementation is available at \url{https://github.com/vios-s/DiffAN} .}, a topological ordering algorithm that leverages DPMs for learning a Hessian function. We introduce theory for updating the learned Hessian without re-training the neural network, and we show that computing with a subset of samples gives an accurate approximation of the ordering, which allows scaling to datasets with more samples and variables. We show empirically that our method scales exceptionally well to datasets with up to $500$ nodes and up to $10^5$ samples while still performing on par over small datasets with state-of-the-art causal discovery methods. Implementation is available at https://github.com/vios-s/DiffAN .

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。

↑