几何因果模型

中文摘要 AI 辅助

科学家通常需要从非独立同分布的结构化数据（例如空间数据、网络数据或分子数据）中得出因果推断。本文提出几何因果模型（GCMs），这是一种针对相依数据的因果推断框架，可利用数据生成过程的底层对称性开展分析。例如，针对空间数据，我们考虑具有平移对称性的过程；针对图数据，我们考虑具有节点置换对称性的过程。本文展示了以群论形式化表述的对称性如何助力因果识别与估计：我们借助顺从群的遍历理论确立识别性，结合几何深度学习与可扩展贝叶斯方法完成估计。当数据为序列且对称性为置换等变性时，该框架可还原独立同分布因果模型与do演算；当采用其他结构与对称性时，可得到全新类型的因果模型。作为示例，我们构建了满足DNA对称性的因果模型，该GCM结合描述结果的深度功能基因组学模型与描述倾向性的DNA语言模型，可得到遗传变异效应的新型估计器，我们在半合成数据上对其进行了验证。

英文摘要

Scientists often seek to draw causal inferences from structured data that is not independently and identically distributed, such as spatial data, network data, or molecular data. We develop geometric causal models (GCMs), a framework for causal inference from dependent data that exploits underlying symmetries of the data generating process. For example, in spatial data, we consider processes that are symmetric under translations, or in graph data, symmetric under permutations of the nodes. We show how symmetries, formalized with group theory, can enable causal identification and estimation. We deploy ergodic theory for amenable groups to establish identification, and combine geometric deep learning with scalable Bayesian inference for estimation. We recover i.i.d. causal models and do-calculus when the data is a sequence and the symmetry is permutation equivariance, and find novel types of causal models when we use alternate structures and symmetries. As an example, we construct a causal model that satisfies the symmetries of DNA. This GCM enables new estimators for the effects of genetic variation, combining deep functional genomics models to describe outcomes and DNA language models to describe propensities. We illustrate on semisynthetic data.

发表机构

• Department of Chemistry, Technical University of Denmark（丹麦技术大学化学系）
• Departments of Statistics and Computer Science, Columbia University（哥伦比亚大学统计学与计算机科学系）

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