Related papers: Half-trek criterion for generic identifiability of…
Linear structural equation models, which relate random variables via linear interdependencies and Gaussian noise, are a popular tool for modeling multivariate joint distributions. These models correspond to mixed graphs that include both…
Linear structural equation models relate the components of a random vector using linear interdependencies and Gaussian noise. Each such model can be naturally associated with a mixed graph whose vertices correspond to the components of the…
Structural equation models are multivariate statistical models that are defined by specifying noisy functional relationships among random variables. We consider the classical case of linear relationships and additive Gaussian noise terms.…
We consider structural equation models in which variables can be written as a function of their parents and noise terms, which are assumed to be jointly independent. Corresponding to each structural equation model, there is a directed…
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…
We develop a criterion to certify whether causal effects are identifiable in linear structural equation models with latent variables. Linear structural equation models correspond to directed graphs whose nodes represent the random variables…
We consider identifiability of partially linear additive structural equation models with Gaussian noise (PLSEMs) and estimation of distributionally equivalent models to a given PLSEM. Thereby, we also include robustness results for errors…
Despite their popularity, many questions about the algebraic constraints imposed by linear structural equation models remain open problems. For causal discovery, two of these problems are especially important: the enumeration of the…
The discovery of causal relationships from observational data is very challenging. Many recent approaches rely on complexity or uncertainty concepts to impose constraints on probability distributions, aiming to identify specific classes of…
In this paper, we introduce a new identifiability criteria for linear structural equation models, which we call regression identifiability. We provide necessary and sufficient graphical conditions for a directed edge to be regression…
In this paper, we address the problem of identifying linear structural equation models. We first extend the edge set half-trek criterion to cover a broader class of models. We then show that any semi-Markovian linear model can be…
The chain graph model admits both undirected and directed edges in one graph, where symmetric conditional dependencies are encoded via undirected edges and asymmetric causal relations are encoded via directed edges. Though frequently…
Consider jointly Gaussian random variables whose conditional independence structure is specified by a graphical model. If we observe realizations of the variables, we can compute the covariance matrix, and it is well known that the support…
Linear structural equation models represent direct causal effects as directed edges and confounding factors as bidirected edges. An open problem is to identify the causal parameters from correlations between the nodes. We investigate…
This paper characterizes the values of partial regression coefficients, defined as projection coefficients onto the space spanned by explanatory variables, for random variables generated by linear structural equation models using graphical…
A foundational question in the theory of linear compartmental models is how to assess whether a model is structurally identifiable -- that is, whether parameter values can be inferred from noiseless data -- directly from the combinatorics…
The paper concerns the problem of predicting the effect of actions or interventions on a system from a combination of (i) statistical data on a set of observed variables, and (ii) qualitative causal knowledge encoded in the form of a…
Linear structural equation models are multivariate statistical models encoded by mixed graphs. In particular, the set of covariance matrices for distributions belonging to a linear structural equation model for a fixed mixed graph $G=(V,…
In this work, we consider the identifiability assumption of Gaussian linear structural equation models (SEMs) in which each variable is determined by a linear function of its parents plus normally distributed error. It has been shown that…
Linear causal models are important tools for modeling causal dependencies and yet in practice, only a subset of the variables can be observed. In this paper, we examine the parameter identifiability of these models by investigating whether…