Multi-trek separation in Linear Structural Equation Models

Half-trek criterion for generic identifiability of linear structural equation models

A linear structural equation model relates random variables of interest and corresponding Gaussian noise terms via a linear equation system. Each such model can be represented by a mixed graph in which directed edges encode the linear equations and bidirected edges indicate possible correlations among noise terms. We study parameter identifiability in these models, that is, we ask for conditions that ensure that the edge coefficients and correlations appearing in a linear structural equation model can be uniquely recovered from the covariance matrix of the associated distribution. We treat the…

过程图上的因果推断，第一部分：结构方程过程表示

Causal Inference on Process Graphs, Part I: The Structural Equation Process Representation

本研究将含潜在分量的递归SVAR过程重构为过程图上的线性过程SCM，推广路径与迹规则，推导频域因果效应表达式并给出识别准则与恢复方法。

Half-Trek Criterion for Identifiability of Latent Variable Models

We consider linear structural equation models with latent variables and develop a criterion to certify whether the direct causal effects between the observable variables are identifiable based on the observed covariance matrix. Linear structural equation models assume that both observed and latent variables solve a linear equation system featuring stochastic noise terms. Each model corresponds to a directed graph whose edges represent the direct effects that appear as coefficients in the equation system. Prior research has developed a variety of methods to decide identifiability of direct effe…

Incorporating Knowledge into Structural Equation Models using Auxiliary Variables

In this paper, we extend graph-based identification methods by allowing background knowledge in the form of non-zero parameter values. Such information could be obtained, for example, from a previously conducted randomized experiment, from substantive understanding of the domain, or even an identification technique. To incorporate such information systematically, we propose the addition of auxiliary variables to the model, which are constructed so that certain paths will be conveniently cancelled. This cancellation allows the auxiliary variables to help conventional methods of identification (…

Algebraic Problems in Structural Equation Modeling

The paper gives an overview of recent advances in structural equation modeling. A structural equation model is a multivariate statistical model that is determined by a mixed graph, also known as a path diagram. Our focus is on the covariance matrices of linear structural equation models. In the linear case, each covariance is a rational function of parameters that are associated to the edges and nodes of the graph. We statistically motivate algebraic problems concerning the rational map that parametrizes the covariance matrix. We review combinatorial tools such as the trek rule, projection to …

过程图的因果推断，第二部分：因果结构与效应识别

Causal Inference on Process Graphs, Part II: Causal Structure and Effect Identification

本文研究SVAR过程的因果发现与效应估计问题，证明可通过谱密度的代数约束识别过程图的d-、t-分离信息，并提出频域因果效应的有理可识别性概念，验证了图形潜因子半迹准则的适用性。

Constraint-based Causal Discovery for Non-Linear Structural Causal Models with Cycles and Latent Confounders

We address the problem of causal discovery from data, making use of the recently proposed causal modeling framework of modular structural causal models (mSCM) to handle cycles, latent confounders and non-linearities. We introduce σ-connection graphs (σ-CG), a new class of mixed graphs (containing undirected, bidirected and directed edges) with additional structure, and extend the concept of σ-separation, the appropriate generalization of the well-known notion of d-separation in this setting, to apply to σ-CGs. We prove the closedness of σ-separation under marginalisation and conditioning and e…

基于分离的因果图距离度量

Separation-based distance measures for causal graphs

针对因果发现算法输出马尔可夫等价类而非单一图的问题，提出基于分离的距离度量方法，适用于DAGs和MAGs，并通过实验验证其有效性。

Learning Linear Non-Gaussian Graphical Models with Multidirected Edges

In this paper we propose a new method to learn the underlying acyclic mixed graph of a linear non-Gaussian structural equation model given observational data. We build on an algorithm proposed by Wang and Drton, and we show that one can augment the hidden variable structure of the recovered model by learning {\em multidirected edges} rather than only directed and bidirected ones. Multidirected edges appear when more than two of the observed variables have a hidden common cause. We detect the presence of such hidden causes by looking at higher order cumulants and exploiting the multi-trek rule.…

鲁棒检验中Chernoff与凸序最优性之间的结构性分离

A Structural Separation Between Chernoff and Convex-Order Optimality in Robust Testing

本文揭示在鲁棒假设检验中，最不利分布同时最大化所有Chernoff u-亲和性并最小化所有f-散度的等价性在一般情形下失效，通过构造三点概率空间上的反例证明该分离，并给出等价成立的充分条件。

有限高斯混合中分离的几何学

On the Geometry of Separation in Finite Gaussian Mixtures

研究最小成分分离对有限高斯混合参数估计收敛速率的影响，通过构建基于Hellinger下界的统一几何框架，揭示了分离复杂度由成分空间配置驱动，并获得了依赖分离的收敛速率。