  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 over
existing approaches 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.
