### 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.

Original language | English |
---|---|

Pages (from-to) | 1225-1248 |

Number of pages | 24 |

Journal | Journal of Machine Learning Research |

Volume | 12 |

Publication status | Published - Apr 1 2011 |

Externally published | Yes |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Software
- Control and Systems Engineering
- Statistics and Probability
- Artificial Intelligence

### Cite this

*Journal of Machine Learning Research*,

*12*, 1225-1248.

**DirectLiNGAM : A direct method for learning a linear non-gaussian structural equation model.** / Shimizu, Shohei; Inazumi, Takanori; Sogawa, Yasuhiro; Hyvärinen, Aapo; Kawahara, Yoshinobu; Washio, Takashi; Hoyer, Patrik O.; Bollen, Kenneth.

Research output: Contribution to journal › Article

*Journal of Machine Learning Research*, vol. 12, pp. 1225-1248.

}

TY - JOUR

T1 - DirectLiNGAM

T2 - A direct method for learning a linear non-gaussian structural equation model

AU - Shimizu, Shohei

AU - Inazumi, Takanori

AU - Sogawa, Yasuhiro

AU - Hyvärinen, Aapo

AU - Kawahara, Yoshinobu

AU - Washio, Takashi

AU - Hoyer, Patrik O.

AU - Bollen, Kenneth

PY - 2011/4/1

Y1 - 2011/4/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=79955829373&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79955829373&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:79955829373

VL - 12

SP - 1225

EP - 1248

JO - Journal of Machine Learning Research

JF - Journal of Machine Learning Research

SN - 1532-4435

ER -