Least-Squares Independence Regression for Non-Linear Causal Inference under Non-Gaussian Noise

TL;DR

This paper introduces LSIR, a novel causal inference method that models non-linear relationships with non-Gaussian noise, optimizing parameters via cross-validation for improved accuracy over existing methods.

Contribution

The paper proposes LSIR, a new causal inference algorithm that minimizes squared-loss mutual information and allows data-driven parameter tuning, enhancing non-linear causal discovery.

Findings

LSIR outperforms state-of-the-art causal inference methods on real-world datasets.

It effectively learns additive noise models with non-Gaussian noise.

Cross-validation helps prevent overfitting in the model.

Abstract

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.