DirectLiNGAM: A Direct Method for Learning a Linear Non-Gaussian Structural Equation Model
Shohei Shimizu,Takanori Inazumi,Yasuhiro Sogawa,Aapo Hyvärinen,Yoshinobu Kawahara,Takashi Washio,Patrik O. Hoyer,Kenneth A. Bollen +7 more
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In this article, a non-Gaussianity-based method is proposed to estimate the causal ordering and connection strength of a linear acyclic model, which is guaranteed to converge to the right solution within a fixed number of steps if the data strictly follows the model.Abstract:
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.read more
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References
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An introduction to the bootstrap
Bradley Efron,Robert Tibshirani +1 more
TL;DR: This article presents bootstrap methods for estimation, using simple arguments, with Minitab macros for implementing these methods, as well as some examples of how these methods could be used for estimation purposes.
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Structural Equations with Latent Variables
TL;DR: The General Model, Part I: Latent Variable and Measurement Models Combined, Part II: Extensions, Part III: Extensions and Part IV: Confirmatory Factor Analysis as discussed by the authors.
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Causality: models, reasoning, and inference
TL;DR: The art and science of cause and effect have been studied in the social sciences for a long time as mentioned in this paper, see, e.g., the theory of inferred causation, causal diagrams and the identification of causal effects.
Journal ArticleDOI
Independent component analysis, a new concept?
TL;DR: An efficient algorithm is proposed, which allows the computation of the ICA of a data matrix within a polynomial time and may actually be seen as an extension of the principal component analysis (PCA).