Rather,theyare generated by latent variables, such as confounders and mediators, which may themselvesbecausallyrelated.

In causal discovery, linear non-Gaussian acyclic models (LiNGAMs) have been studied extensively. While the causally sufficient case is well understood, in many real problems the observed variables are not causally related. Rather, they are generated by latent variables, such as confounders and mediators, which may themselves be causally related. Existing results on the identification of the causal structure among the latent variables often require very strong graphical assumptions. In this paper, we consider partially observed linear models with either non-Gaussian or heterogeneous errors.

The regular models of a normal logic program are a particular type of partial (i.e. 3-valued) models which correspond to stable partial models with minimal undefinedness. In this paper, we explore graphical conditions on the dependency graph of a finite ground normal logic program to analyze the existence, unicity and number of regular models for the program. We show three main results: 1) a necessary condition for the existence of non-trivial (i.e. non-2-valued) regular models, 2) a sufficient condition for the unicity of regular models, and 3) two upper bounds for the number of regular models based on positive feedback vertex sets. The first two conditions generalize the finite cases of the two existing results obtained by You and Yuan (1994) for normal logic programs with well-founded stratification. The third result is also new to the best of our knowledge. Key to our proofs is a connection that we establish between finite ground normal logic programs and Boolean network theory.

In causal discovery, linear non-Gaussian acyclic models (LiNGAMs) have been studied extensively. While the causally sufficient case is well understood, in many real problems the observed variables are not causally related. Rather, they are generated by latent variables, such as confounders and mediators, which may themselves be causally related. Existing results on the identification of the causal structure among the latent variables often require very strong graphical assumptions. In this paper, we consider partially observed linear models with either non-Gaussian or heterogeneous errors.

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 directed acyclic graph (DAG). The DAG represents a set of linear equations called Structural Equations Model (SEM), whose coefficients are parameters representing direct causal effects. Reliable quantitative conclusions can only be obtained from the model if the causal effects are uniquely determined by the data. That is, if there exists a unique parametrization for the model that makes it compatible with the data. If this is the case, the model is called identified. The main result of the paper is a general sufficient condition for identification of recursive SEM models.

This paper deals with the problem of identifying direct causal effects in recursive linear structural equation models. The paper establishes a sufficient criterion for identifying individual causal effects and provides a procedure computing identified causal effects in terms of observed covariance matrix.