DirectLiNGAM: A Direct Method for Learning a Linear Non-Gaussian Structural Equation Model

By Shohei Shimizu, Takanori Inazumi, Yasuhiro Sogawa, Aapo Hyvärinen, Yoshinobu Kawahara, Takashi Washio, Patrik O. Hoyer, Kenneth A. Bollen. 2011

674 citations recorded by the source corpus.

Structural equation models and Bayesian networks have been widely used to analyze causal relations between continuous variables. In such frameworks, linear acyclic models are typically used to model the data-generating process of variables. Recently, it was shown that use of non-Gaussianity identifies the full structure of a linear acyclic model, that is, a causal ordering of variables and their connection strengths, without using any prior knowledge on the network structure, which is not the case with conventional methods. However, existing estimation methods are based on iterative search algorithms and may not converge to a correct solution in a finite number of steps. In this paper, we propose a new direct method to estimate a causal ordering and connection strengths based on non-Gaussianity. In contrast to the previous methods, our algorithm requires no algorithmic parameters and is guaranteed to converge to the right solution within a small fixed number of steps if the data strictly follows the model, that is, if all the model assumptions are met and the sample size is infinite.

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Citations in the corpus

Distinguishing Cause from Effect Using Observational Data: Methods and Benchmarks (2014, background): “Keywords: Causal discovery, additive noise, information-geometric causal inference, cause-effect pairs, benchmarks”
Causal Discovery with Reinforcement Learning (2019, methodology): “The estimates obtained by ICA-LiNGAM, PC and GES can be found in [22], which either have less correct directed edges or several unoriented edges.”
Causal Structure Learning (2017, methodology): “There is also a diﬀerent implementation called DirectLINGAM (Shimizu et al., 2011) that uses a pairwise causality measure instead of ICA.”
Estimating a Causal Order among Groups of Variables in Linear Models (2012, methodology): “This is formally stated in the following lemma, which corresponds to the combination of Lemma 2 and Corollary 1 in [5].”
Deep Computational Phenotyping (2015, background): “While we do not have such priors available for our labels, we can still identify potential causation among the variables if they are not distributed according to Gaussian distribution [28, 29, 18].”
BCD Nets: Scalable Variational Approaches for Bayesian Causal Discovery (2021, methodology): “To compare against a baseline that is widely used in practice, we also evaluate the DirectLiNGAM method [49], designed for non-Gaussian likelihoods.”
Pairwise Likelihood Ratios for Estimation of Non-Gaussian Structural Equation Models (2013, methodology): “5 • DirectLiNGAM, specifically the kernel-based version proposed by Shimizu et al. (2011).”
Distinguishing Cause from Effect Using Observational Data: Methods and Benchmarks (2014, background): “Keywords: Causal discovery, additive noise, information-geometric causal inference, cause-effect pairs, benchmarks”
Causal discovery in heavy-tailed models (2019, methodology): “DirectLiNGAM, introduced by Shimizu et al. (2011), is an algorithm based on two iterative steps, namely, finding an exogenous variable (i.e., a node in the DAG with no parents), and regressing this variable out of all the others.”
Structure Learning in Graphical Modeling (2016, background): “Shimizu et al. (2011) give a more advanced implementation that is suitable for larger numbers of variables.”
High-dimensional learning of linear causal networks via inverse covariance estimation (2013, methodology): “Deviating slightly from the literature, we use the term non-Gaussian to refer to the fact that the variables are not jointly Gaussian; however, we do not require non-Gaussianity of all exogenous noise variables, as assumed by Shimizu et al. (2011).”
Review of Causal Discovery Methods Based on Graphical Models (2019, methodology): “Another way to reduce the estimation error is to ﬁnd the causal ordering by recursively performing regression and independence test between the predictor and residual, as done by DirectLiNGAM (Shimizu et al., 2011).”
Towards a Learning Theory of Cause-Effect Inference (2015, background): “First, the linear non-Gaussian causal model (Shimizu et al., 2006; 2011) recovers the true causal direction between two variables whenever their relationship is linear and polluted with additive and non-Gaussian noise.”
UvA-DARE ( Digital Academic Repository ) Causal Discovery with Continuous Additive Noise Models (2014, unknown): “Later, improved versions of this method have been proposed in (Shimizu et al., 2011; Hyvärinen and Smith, 2013).”