LiNGAM — Discovery of Non-Gaussian Linear Causal Models

Brief description

LiNGAM (Linear Non-Gaussian Acyclic Model) is a framework for discovering causal structure from continuous-valued observational data.

The basic model assumes linear relationships, an acyclic causal structure, no unobserved confounders, and mutually independent, non-Gaussian error terms. Under these assumptions, the causal ordering and connection strengths are identifiable.

Extensions address time series, latent confounders, cyclic structures, and nonlinear relationships. 

Original article

S. Shimizu, P. O. Hoyer, A. Hyvärinen, and A. Kerminen.
A Linear Non-Gaussian Acyclic Model for Causal Discovery.
Journal of Machine Learning Research, 7: 2003–2030, 2006.
paper

Selected methods

DirectLiNGAM

S. Shimizu, T. Inazumi, Y. Sogawa, A. Hyvärinen, Y. Kawahara, T. Washio, P. O. Hoyer, and K. Bollen.
DirectLiNGAM: A Direct Method for Learning a Linear Non-Gaussian Structural Equation Model.
Journal of Machine Learning Research, 12: 1225–1248, 2011.
paper

Pairwise LiNGAM

A. Hyvärinen and S. M. Smith.
Pairwise Likelihood Ratios for Estimation of Non-Gaussian Structural Equation Models.
Journal of Machine Learning Research, 14: 111–152, 2013.
paper

VAR-LiNGAM

A. Hyvärinen, K. Zhang, S. Shimizu, and P. O. Hoyer.
Estimation of a Structural Vector Autoregression Model Using Non-Gaussianity.
Journal of Machine Learning Research, 11: 1709–1731, 2010.
paper

Hidden common causes

P. O. Hoyer, S. Shimizu, A. J. Kerminen, and M. Palviainen.
Estimation of causal effects using linear non-gaussian causal models with hidden variables.
International Journal of Approximate Reasoning, 49: 362-378, 2008.
paper

Nonlinearity

P. O. Hoyer, D. Janzing, J. Mooij, J. Peters, and B. Schölkopf. 

Nonlinear causal discovery with additive noise models. 

Advances in Neural Information Processing Systems 21 (NIPS2008), pp. 689-696, 2009.

paper

Papers on LiNGAM and related methods

Collected bibliographic lists covering basic models, extensions, related methods, applications, reviews, and software — PDF

Software

Created at the Neuroinformatics group in University of Helsinki around 2006