Pairwise Likelihood Ratios for Estimation of Non-Gaussian Structural Equation Models

By Aapo Hyvärinen, Stephen M. Smith. 2013

215 citations recorded by the source corpus.

We present new measures of the causal direction, or direction of effect, between two non-Gaussian random variables. They are based on the likelihood ratio under the linear non-Gaussian acyclic model (LiNGAM). We also develop simple first-order approximations of the likelihood ratio and analyze them based on related cumulant-based measures, which can be shown to find the correct causal directions. We show how to apply these measures to estimate LiNGAM for more than two variables, and even in the case of more variables than observations. We further extend the method to cyclic and nonlinear models. The proposed framework is statistically at least as good as existing ones in the cases of few data points or noisy data, and it is computationally and conceptually very simple. Results on simulated fMRI data indicate that the method may be useful in neuroimaging where the number of time points is typically quite small.

Subfields: Artificial Intelligence, Cognitive Neuroscience, Signal Processing

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Citations in the corpus

Distinguishing Cause from Effect Using Observational Data: Methods and Benchmarks (2014, background): “…Hyvärinen, 2009; Janzing et al., 2010; Mooij et al., 2010; Daniušis et al., 2010; Mooij et al., 2011; Shimizu et al., 2011; Janzing et al., 2012; Hyvärinen and Smith, 2013; Peters and Bühlmann, 2014; Kpotufe et al., 2014; Nowzohour and Bühlmann, 2015; Sgouritsa et al., 2015) that were…”
Independent component analysis: recent advances (2013, methodology): “A more eﬃcient way of choosing between the models can be based on likelihood ratios of the two models (Hyvärinen, 2010; Hyvärinen and Smith, 2011).”
Causal Discovery with General Non-Linear Relationships using Non-Linear ICA (2019, methodology): “In this sense NonSENS is more closely aligned to the Pairwise LiNGAM method (Hyvärinen and Smith, 2013).”
Deep Computational Phenotyping (2015, methodology): “We find the causal edges between each feature and label using the state-of-the-art Pairwise LiNGAM algorithm from [18].”
Distinguishing Cause from Effect Using Observational Data: Methods and Benchmarks (2014, background): “…Hyvärinen, 2009; Janzing et al., 2010; Mooij et al., 2010; Daniušis et al., 2010; Mooij et al., 2011; Shimizu et al., 2011; Janzing et al., 2012; Hyvärinen and Smith, 2013; Peters and Bühlmann, 2014; Kpotufe et al., 2014; Nowzohour and Bühlmann, 2015; Sgouritsa et al., 2015) that were…”
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).”
Score-based causal learning in additive noise models (2013, methodology): “Two other score-based methods have recently been proposed: for the parametric setting of Gaussian and linear models with same error variances [Peters and B¨uhlmann, 2012] and for linear models with non-Gaussian noise [Hyv¨arinen and Smith, 2013].”
Non-linear Causal Inference using Gaussianity Measures (2014, methodology): “Similar results have been obtained in the case of nonlinear relations and the univariate data case (Hyvärinen and Smith, 2013; Kpotufe et al., 2014).”
Cause-Effect Inference by Comparing Regression Errors (2018, methodology): “For the experiments, we used a state-of-the-art implementation based on [25].”
Generalized Score Functions for Causal Discovery (2018, methodology): “More recently, some other score-based methods [2, 4, 18, 19, 26] and hybrid methods [9, 31] have been proposed; they exploit some assumptions of the model class.”
D’ya Like DAGs? A Survey on Structure Learning and Causal Discovery (2021, methodology): “Common scoring functions include the Bayesian Information Criterion (BIC) [66], the Minimum Description Length (as an approximation of Kolmogorov Complexity) [82, 114, 121], the Bayesian Gaussian equivalent (BGe) score [66], the Bayesian Dirichlet equivalence (BDe) score [91], the Bayesian Dirichlet”