A Linear Non-Gaussian Acyclic Model for Causal Discovery

By Shohei Shimizu, Patrik O. Hoyer, Aapo Hyvärinen, Antti J. Kerminen. 2006

2,034 citations recorded by the source corpus.

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In Causal Inference & Discovery

Citations in the corpus

Gradient-Based Neural DAG Learning (2019, background): “There are many examples of graph identifiability results for continuous variables [11, 9, 14, 17] as well as for discrete variables [10].”
Toward Causal Representation Learning (2021, background): “[229] for linear functions, and it can be generalized to include nonlinear rescalings [279], loops [174], confounders [123], and multivariable settings [189].”
Towards Causal Representation Learning (2021, background): “[237, 188, 229, 113, 174, 187, 139, 17, 246, 277, 175, 123, 186, 176, 36, 82, 161], learning causal relations frequently requires collecting data from multiple environments, or the ability to perform interventions [251].”
Sample-Efficient Reinforcement Learning via Counterfactual-Based Data Augmentation (2020, background): “, linear relations [13], nonlinear relations with additive noise [14], or the causal model with further post-nonlinear transformations [15].”
Causality for Machine Learning (2019, background): “It generalizes results of Shimizu et al. (2006) for linear functions, and it can be generalized to include nonlinear rescalings (Zhang and Hyvärinen, 2009), loops (Mooij et al., 2011), confounders (Janzing et al., 2009), and multi-variable settings (Peters et al., 2011).”
Learning Neural Causal Models from Unknown Interventions (2019, methodology): “…based on observational data (Chickering, 2002; Tsamardinos et al., 2006; Goudet et al., 2017; Hauser & Bühlmann, 2012; Spirtes et al., 2000; Sun et al., 2007; Zhang et al., 2012; Shimizu et al., 2006; Hoyer et al., 2009; Daniusis et al., 2012; Budhathoki & Vreeken, 2017; Kalainathan et al., 2018).”
Causal Discovery from Heterogeneous/Nonstationary Data (2019, methodology): “, additive (Shimizu et al., 2006; Hoyer et al., 2009; Zhang and Hyvärinen, 2009a) and post-nonlinear models (Zhang and Chan, 2006; Zhang and Hyvärinen, 2009b).”
Causal Generative Neural Networks (2017, methodology): “We compare CGNN to the PC algorithm [Spirtes et al. , 2000], the score-based methods GES [Chickering, 2002], LiNGAM [Shimizu et al. , 2006], causal additive model (CAM) [Peters et al. , 2014] and with the pairwise methods ANM and Jarfo.”
Causal Discovery from Temporally Aggregated Time Series (2017, methodology): “When the error terms are non-Gaussian, it has the same form as the Linear, Non-Gaussian Model (LiNG) (Lacerda et al., 2008); when the causal relations are further assumed to be acyclic, it follows the form of the Linear, Non-Gaussian Acyclic Model (LiNGAM) (Shimizu et al., 2006).”
Causal Discovery from Nonstationary/Heterogeneous Data: Skeleton Estimation and Orientation Determination (2017, neutral): “…there is only one conditional independence relationship, Moreover, when one ﬁts a ﬁxed functional causal model (e.g., the linear, non-Gaussian model [Shimizu et al. , 2006], the additive noise model [Hoyer et al. , 2009; Zhang and Hyv¨arinen, 2009a], or the post-nonlinear causal model [Zhang and…”
Invariant Causal Prediction for Nonlinear Models (2017, background): “Such assumptions include non-Gaussianity (Shimizu et al., 2006) or equal variances (Peters and B¨uhlmann, 2014) of the errors or non-linearity of the structural equations in additive noise models (Hoyer et al., 2009; Peters et al., 2014).”
Invariant Causal Prediction for Sequential Data (2017, methodology): “Many procedures in this field only use observational data (e.g., Spirtes, Glymour, and Scheines 2000; Chickering 2002; Shimizu et al. 2006; Janzing et al. 2012; van de Geer and Bühlmann 2013; Peters et al. 2014; Bühlmann, Peters, and Ernest 2014).”
Group invariance principles for causal generative models (2017, neutral): “While we showed in previous sections that several ICM-based approaches fit in our group theoretic framework, it can also be related to other causal inference methods such as LiNGAM (Shimizu et al., 2006), which relies on the assumption that the additive noise of a causal mechanism is independent fro”
The Arrow of Time in Multivariate Time Series (2016, methodology): “If the generated graph is time consistent in the sense that all links go from lower to higher labeled variables (or the opposite), LiNGAM proposes this direction as the correct one.”
Identifiability of Causal Graphs using Functional Models (2011, background): “If one further uses linear ANMs F = F1, for example, and restricts B to contain only non-Gaussian noise, also (3) holds and we recover LiNGAM [Shimizu et al., 2006].”
Distinguishing Cause from Effect Using Observational Data: Methods and Benchmarks (2014, methodology): “This means that whenever we can model an observational distribution PX,Y with a model of the form (3), we can also model it using (2), and therefore the causal relationship between X and Y is not identifiable from the observational distribution without making additional assumptions.”
On the Identifiability of the Post-Nonlinear Causal Model (2009, methodology): “For example, under the condition that causal relations are linear and acyclic, the non-Gaussianity of the disturbances could help find the whole causal model uniquely (Shimizu et al., 2006), by resorting to the independent component analysis (ICA) technique (Hyvärinen et al.”
CAM: Causal Additive Models, high-dimensional order search and penalized regression (2013, methodology): “…of our method to greedy equivalence search (GES) (Chickering, 2002), the PC algorithm (Spirtes et al., 2000), the conservative PC algorithm (CPC) (Ramsey et al., 2006), LiNGAM (Shimizu et al., 2006) and regression with subsequent independence tests (RESIT) (Mooij et al., 2009; Peters et al., 2013).”