Lingam: Non-Gaussian Methods for Estimating Causal Structures

Abstract

In many empirical sciences, the causal mechanisms underlying various phenomena need to be studied. Structural equation modeling is a general framework used for multivariate analysis, and provides a powerful method for studying causal mechanisms. However, in many cases, classical structural equation modeling is not capable of estimating the causal directions of variables. This is because it explicitly or implicitly assumes Gaussianity of data and typically utilizes only the covariance structure of data. In many applications, however, non-Gaussian data are often obtained, which means that more information may be contained in the data distribution than the covariance matrix is capable of containing. Thus, many new methods have recently been proposed for utilizing the non-Gaussian structure of data and estimating the causal directions of variables. In this paper, we provide an overview of such recent developments in causal inference, and focus in particular on the non-Gaussian methods known as LiNGAM.

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.…”

Causal discovery algorithms: A practical guide

“…Finally, causal search algorithms with semi‐parametric assumptions use these additional assumptions to learn causal relationships more efficiently or in more detail. For example, when the data are generated by linear mechanisms but with non‐Gaussian noise, Linear Non‐Gaussian Model (LiNGaM) algorithms can recover the DAG structure using a signal analysis technique called independent components analysis (Shimizu, provides an overview). Some techniques in this category can even account for “feedback” loops of different types (Lacerda, Spirtes, Ramsey, & Hoyer, ) or latent common cause variables (Hoyer, Shimizu, Kerminen, & Palviainen, ).…”

“…Finally, causal search algorithms with semi-parametric assumptions use these additional assumptions to learn causal relationships more efficiently or in more detail. For example, when the data are generated by linear mechanisms but with non-Gaussian noise, Linear Non-Gaussian Model (LiNGaM) algorithms can recover the DAG structure using a signal analysis technique called independent components analysis (Shimizu, 2014 provides an overview).…”

Special feature: recent developments in causal discovery and inference

“…The objective of this special feature is to present an up-to-date overview of causal discovery and inference methods with an emphasis on their applications, unlike a previous special issue on causal discovery in Behaviormetrika that focused on its methodological aspects (Ilya et al 2014;Tillman and Eberhardt 2014;Shimizu 2014).…”

“…The objective of this special feature is to present an up-to-date overview of causal discovery and inference methods with an emphasis on their applications, unlike a previous special issue on causal discovery in Behaviormetrika that focused on its methodological aspects (Ilya et al 2014;Tillman and Eberhardt 2014;Shimizu 2014).The Behaviormetrika editorial board invited the following three survey papers, which present some interesting topics related to causal discovery and inference. All the three papers were reviewed by two or three reviewers to elicit suggestions for possible improvements in their presentation.…”