Estimation of linear non-Gaussian acyclic models for latent factors

Direction of dependence in measurement error models

“…Relation to causal search Using higher moments of measurement error-prone variables to infer on data-generating mechanisms has also been discussed in the context of causal search algorithms (for overviews, see Shimizu, 2014Shimizu, , 2016Spirtes & Zhang, 2016). Shimizu, Hoyer, and Hyv€ arinen (2009) proposed a causal discovery algorithm to deduce directional statements concerning latent factors of observed variables by combining the BuildPureCluster algorithm (Silva, Scheine, Glymour, & Spirtes, 2006), which identifies the number of latent factors and their 'pure' measurement variables (i.e., those measurement variables that emerge from a single latent factor), with the linear non-Gaussian acyclic model (LiNGAM; Shimizu, Hoyer, Hyv€ arinen, & Kerminen, 2006), a causal search algorithm that discovers directed acyclic graph structures beyond Markov equivalence classes. Compared to Shimizu et al's (2009) algorithm, the present approach differs both conceptually and methodologically.…”

“…Shimizu, Hoyer, and Hyv€ arinen (2009) proposed a causal discovery algorithm to deduce directional statements concerning latent factors of observed variables by combining the BuildPureCluster algorithm (Silva, Scheine, Glymour, & Spirtes, 2006), which identifies the number of latent factors and their 'pure' measurement variables (i.e., those measurement variables that emerge from a single latent factor), with the linear non-Gaussian acyclic model (LiNGAM; Shimizu, Hoyer, Hyv€ arinen, & Kerminen, 2006), a causal search algorithm that discovers directed acyclic graph structures beyond Markov equivalence classes. Compared to Shimizu et al's (2009) algorithm, the present approach differs both conceptually and methodologically. From a conceptual perspective, Wiedermann and von Eye (2015c) suggest sharply distinguishing between causal search algorithms (which carry a major exploratory element and are thus suited to generating new hypotheses) and the direction dependence methodology (a confirmatory approach to probing a theory-based hypothesis about directionality).…”

“…From a conceptual perspective, Wiedermann and von Eye (2015c) suggest sharply distinguishing between causal search algorithms (which carry a major exploratory element and are thus suited to generating new hypotheses) and the direction dependence methodology (a confirmatory approach to probing a theory-based hypothesis about directionality). From a methodological perspective, Shimizu et al's (2009) method makes use of independent component analysis (ICA; Hyv€ arinen, Karhunen, & Oja, 2001) with additive errors (noisy ICA) to estimate model parameters, while the present approach relies on parameter estimation based on higher moments of observed variables. Further, Shimizu et al's (2009) approach assumes that each latent factor has at least three pure measurement variables.…”

“…From a methodological perspective, Shimizu et al's (2009) method makes use of independent component analysis (ICA; Hyv€ arinen, Karhunen, & Oja, 2001) with additive errors (noisy ICA) to estimate model parameters, while the present approach relies on parameter estimation based on higher moments of observed variables. Further, Shimizu et al's (2009) approach assumes that each latent factor has at least three pure measurement variables. The present approach, in contrast, can be used when only one observed variable is available per latent factor.…”

Learning causality and causality-related learning: some recent progress

“…Thanks to the constrained functional classes, the causal direction between X and Y is identifiable because the independence condition between the noise and cause holds only for the true causal direction and is violated for the wrong direction (for details one may see [3]). Typical FCMs include the linear, non-Gaussian, acyclic model (LiNGAM) [4], in which Y = aX + E with linear coefficient a , the nonlinear additive noise model (ANM) [5], in which Y = f ( X ) + E , and the post-nonlinear (PNL) causal model [6], which further considers possible nonlinear sensor or measurement distortion f 2 in the causal process: Y = f 2 ( f 1 ( X ) + E ).…”