发表机构
Tongji University（同济大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出一种基于条件协方差算子范数比较的混合回归方法，用于函数变量的因果发现，无需结构或分布假设，并能估计DAG，在模拟和真实脑连接数据中表现良好。
AI 中文摘要
我们研究每个节点均为随机函数的因果发现。以往关于此主题的研究依赖于结构性假设（如线性或非线性）和分布性假设（如高斯或非高斯）。相比之下，我们利用协方差算子来避免这些假设。在函数加性噪声模型下，我们提出了一个新的充分条件，通过比较条件协方差算子的范数来识别有效的拓扑排序。利用这一可识别性条件，我们开发了一个新的混合回归模型，该模型涵盖了线性和非线性模型。结合变量选择，我们的方法能够估计函数变量的因果有向无环图（DAG）。理论上，我们发展了该回归模型的最小二乘型理论，并推导了阶数确定、稀疏回归以及识别DAG的渐近一致性。提供了基于离散观测的计算算法。应用于模拟数据，我们的方法在现有方法中表现令人满意。还给出了一个大脑有效连接的真实数据示例。
英文摘要
We study causal discovery where each node is a random function. Previous studies on this topic rely on structural assumptions, e.g., linearity or non-linearity, and distributional assumptions, e.g., Gaussianity or non-Gaussianity. In contrast, we make use of covariance operators to avoid these assumptions. Under functional additive noise models, we propose a new sufficient condition to identify a valid topological ordering based on comparing norms of conditional covariance operators. Taking advantage of this identifiability condition, we develop a new mixed regression model that subsumes linear and non-linear models. Together with variable selection, our procedure yields an estimation of the causal directed acyclic graph (DAG) for functional variables. In theory, we develop the least-squares-type theory of this regression model, and derive asymptotic consistency of order determination, sparse regression, as well as identifying the DAG. Computational algorithms based on discrete observations are provided. Applied to simulated data, our approach performs satisfactorily among existing approaches. A real data example of brain effective connectivity is also presented.
