Estimation of causal effects using linear non-Gaussian causal models with hidden variables

By Patrik O. Hoyer, Shohei Shimizu, Antti J. Kerminen, Markus Palviainen. 2008

243 citations recorded by the source corpus.

The task of estimating causal effects from non-experimental data is notoriously difficult and unreliable. Nevertheless, precisely such estimates are commonly required in many fields including economics and social science, where controlled experiments are often impossible. Linear causal models (structural equation models), combined with an implicit normality (Gaussianity) assumption on the data, provide a widely used framework for this task. We have recently described how non-Gaussianity in the data can be exploited for estimating causal effects. In this paper we show that, with non-Gaussian data, causal inference is possible even in the presence of hidden variables (unobserved confounders), even when the existence of such variables is unknown a priori. Thus, we provide a comprehensive and complete framework for the estimation of causal effects between the observed variables in the linear, non-Gaussian domain. Numerical simulations demonstrate the practical implementation of the proposed method, with full Matlab code available for all simulations.

Subfields: Analytical Chemistry, Electrochemistry, Signal Processing

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Citations in the corpus

Causal Regularization (2019, background): “[17] constructs confounders for linear non-Gaussian models and [18] infer confounders of univariate X,Y subject to the additive noise assumption.”
Semi-supervised learning, causality, and the conditional cluster assumption (2019, background): “Ycan nonetheless introduce such dependence due to its shared inﬂuence on the two distributions: P(X C) = R P(X CjH)dP(H); P(YjX C) = R P(YjX C;H)dP(H): Methods for detecting hidden confounding (e.g., Hoyer et al., 2008; Janzing and Sch¨olkopf, 2018) can potentially help identify such confounded caus”
Distinguishing Cause from Effect Using Observational Data: Methods and Benchmarks (2014, methodology): “Full identifiability in the presence of hidden variables for the acyclic case has only been established for linear non-Gaussian models (Hoyer et al., 2008).”
Identifying confounders using additive noise models (2009, methodology): “Under the assumption of linear relationships between variables, confounders may be identified by means of Independent Component Analysis, as shown recently by Hoyer et al. [2008], if the distributions are non-Gaussian. Other results for the linear case are presented in Silva et al. [2006]. In this p”
Causal Structure Learning (2017, methodology): “There are various modiﬁcations of LINGAM, for example to allow for hidden variables (Hoyer et al., 2008) or cycles (Lacerda et al., 2008).”
Discovering Cyclic Causal Models with Latent Variables: A General SAT-Based Procedure (2013, unknown): “2008)).”
Estimation of a Structural Vector Autoregression Model Using Non-Gaussianity (2010, methodology): “(The case of latent variables, that is, unobserved confounders, was later considered by Hoyer et al., 2008.)”
Distinguishing Cause from Effect Using Observational Data: Methods and Benchmarks (2014, background): “Full identifiability in the presence of hidden variables for the acyclic case has only been established for linear non-Gaussian models (Hoyer et al., 2008).”
Causal Discovery and Inference: Concepts and Recent Methodological Advances (2016, methodology): “It is worth mentioning that in the linear case, it is possible to further estimate the effect of the underlying confounders in the system, if there are any, by exploiting over-complete ICA (which allows more independent sources than observed variables) (Hoyer et al. 2008).”
DirectLiNGAM: A Direct Method for Learning a Linear Non-Gaussian Structural Equation Model (2011, background): “We note that each bij represents the direct causal effect of xj on xi and each aij , the (i, j)-the element of the matrix A=(I−B), the total causal effect of xj on xi [17].”
Estimating Causal Direction and Confounding of Two Discrete Variables (2016, background): “1, although Hoyer et al. (2008) have extended the linear non-Gaussian methods to the general hypothesis space of Fig, 1 and Janzing et al. (2009) showed that the additive noise assumption can be used to detect pure confounding with some success, i.e. to distinguish hypothesis B from hypotheses C…”
UvA-DARE ( Digital Academic Repository ) Causal Discovery with Continuous Additive Noise Models (2014, unknown): “Proof The proof of Hoyer et al. (2009) is reproduced in Appendix A.”
Review of Causal Discovery Methods Based on Graphical Models (2019, background): “It is worth mentioning that in the linear case, it is possible to further estimate the effect of the underlying confounders in the system, if there are any, by exploiting overcomplete ICA (which allows more independent sources than observed variables) (Hoyer et al., 2008).”