[Paper Review] Learning Linear Non-Gaussian Causal Models in the Presence of Latent Variables

Saber Salehkaleybar, AmirEmad Ghassami+2 more|arXiv (Cornell University)|Aug 11, 2019

Bayesian Modeling and Causal Inference12 citations

TL;DR

This paper proposes a method to learn linear non-Gaussian causal models with latent variables by identifying causal orders and computing all possible causal effects compatible with observational data. It provides graphical conditions for unique identification of causal effects and total effects, showing that uniqueness is generally not possible without structural constraints, but can be achieved under specific conditions on the causal graph.

ABSTRACT

We consider the problem of learning causal models from observational data generated by linear non-Gaussian acyclic causal models with latent variables. Without considering the effect of latent variables, one usually infers wrong causal relationships among the observed variables. Under faithfulness assumption, we propose a method to check whether there exists a causal path between any two observed variables. From this information, we can obtain the causal order among them. The next question is then whether or not the causal effects can be uniquely identified as well. It can be shown that causal effects among observed variables cannot be identified uniquely even under the assumptions of faithfulness and non-Gaussianity of exogenous noises. However, we will propose an efficient method to identify the set of all possible causal effects that are compatible with the observational data. Furthermore, we present some structural conditions on the causal graph under which we can learn causal effects among observed variables uniquely. We also provide necessary and sufficient graphical conditions for unique identification of the number of variables in the system. Experiments on synthetic data and real-world data show the effectiveness of our proposed algorithm on learning causal models.

Motivation & Objective

• To address the challenge of learning causal structures from observational data when latent confounders are present in linear non-Gaussian acyclic models.
• To determine whether causal effects among observed variables can be uniquely identified in the presence of latent variables.
• To develop a method that computes the full set of possible causal effects compatible with the data, rather than assuming uniqueness.
• To derive necessary and sufficient graphical conditions under which causal effects among observed variables can be uniquely identified.
• To provide conditions for the unique identification of the total number of variables in the system, including latent ones.

Proposed method

• The method checks for the existence of a causal path between any two observed variables under the faithfulness assumption, enabling causal order inference.
• It formulates the problem as an overcomplete ICA problem to recover latent structures and causal effects from observational data.
• The approach computes the set of all possible causal effects that are observationally equivalent, using path-based decomposition of total effects.
• It introduces a path-weighting formalism where total causal effects are computed as sums over all causal paths, with weights defined by edge coefficients.
• Graphical conditions are derived based on the structure of the causal graph to determine when causal effects are uniquely identifiable.
• The method uses iterative regression and independence testing to detect confounding and identify root/sink variables, even in the presence of latent confounders.

Experimental results

Research questions

• RQ1 Can we reliably determine the causal order among observed variables when latent confounders are present in a linear non-Gaussian model?
• RQ2 Are causal effects among observed variables uniquely identifiable from observational data under non-Gaussianity and faithfulness?
• RQ3 What structural conditions on the causal graph allow for unique identification of causal effects in the presence of latent variables?
• RQ4 Can we compute the full set of all possible causal effects that are compatible with the observed data?
• RQ5 What conditions are necessary and sufficient for uniquely identifying the total number of variables in the system, including latent ones?

Key findings

• Causal effects among observed variables cannot be uniquely identified even under faithfulness and non-Gaussianity assumptions, due to the presence of latent confounders.
• The paper provides a complete characterization of all possible causal effects compatible with the data, forming a set of solutions rather than a unique one.
• Under specific structural conditions—such as the absence of certain path configurations—unique identification of causal effects becomes possible.
• The total number of variables in the system, including latent ones, can be uniquely identified if and only if the causal graph satisfies certain graphical constraints.
• Experiments on synthetic and real-world data demonstrate that the proposed algorithm effectively recovers causal structures and identifies the correct set of compatible causal effects.