标题： 线性非高斯模型中不相交环的因果发现 显示英文标题

标题： Causal Discovery for Linear Non-Gaussian Models with Disjoint Cycles

摘要： 线性结构方程建模的范式很容易允许在模型规范中包含因果反馈回路。 这些在模型的常见图形表示中表现为有向环。 然而，环的存在会带来一些困难，例如模型可能不再由条件独立关系来表征。 因此，学习循环因果结构仍然是一个具有挑战性的问题。 在本文中，我们在线性非高斯模型的背景下对这一问题提供了新的见解。 首先，我们精确地描述了何时两个有向图决定了同一个线性非高斯模型。 接下来，我们考虑了一种环不相交的图的情况，对于这种情形，我们能够证明非高斯分布的低阶矩之间的简单二次和三次多项式关系可以用来定位源环。 结合一种消除环相关性的策略和多元回归，可以推断出有向环之间的块拓扑顺序，这导致了一个{一致且计算高效的算法}来学习具有不相交环的因果结构。 显示英文摘要

摘要： The paradigm of linear structural equation modeling readily allows one to incorporate causal feedback loops in the model specification. These appear as directed cycles in the common graphical representation of the models. However, the presence of cycles entails difficulties such as the fact that models need no longer be characterized by conditional independence relations. As a result, learning cyclic causal structures remains a challenging problem. In this paper, we offer new insights on this problem in the context of linear non-Gaussian models. First, we precisely characterize when two directed graphs determine the same linear non-Gaussian model. Next, we take up a setting of cycle-disjoint graphs, for which we are able to show that simple quadratic and cubic polynomial relations among low-order moments of a non-Gaussian distribution allow one to locate source cycles. Complementing this with a strategy of decorrelating cycles and multivariate regression allows one to infer a block-topological order among the directed cycles, which leads to a {consistent and computationally efficient algorithm} for learning causal structures with disjoint cycles.