Machine Learning

, Volume 96, Issue 3, pp 249–267

Least-squares independence regression for non-linear causal inference under non-Gaussian noise


DOI: 10.1007/s10994-013-5423-y

Cite this article as:
Yamada, M., Sugiyama, M. & Sese, J. Mach Learn (2014) 96: 249. doi:10.1007/s10994-013-5423-y


The discovery of non-linear causal relationship under additive non-Gaussian noise models has attracted considerable attention recently because of their high flexibility. In this paper, we propose a novel causal inference algorithm called least-squares independence regression (LSIR). LSIR learns the additive noise model through the minimization of an estimator of the squared-loss mutual information between inputs and residuals. A notable advantage of LSIR is that tuning parameters such as the kernel width and the regularization parameter can be naturally optimized by cross-validation, allowing us to avoid overfitting in a data-dependent fashion. Through experiments with real-world datasets, we show that LSIR compares favorably with a state-of-the-art causal inference method.


Causal inference Non-linear Non-Gaussian Squared-loss mutual information Least-squares independence regression 

Copyright information

© The Author(s) 2013

Authors and Affiliations

  1. 1.701 1st Ave.SunnyvaleUSA
  2. 2.TokyoJapan

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