Regression by dependence minimization and its application to causal inference
Joris Mooij, Dominik Janzing, Jonas Peters and Bernhard Schölkopf
In: The 26th International Conference on Machine Learning (ICML 2009), 14-18 Jun 2009, Montreal, Canada.
Motivated by causal inference problems, we propose a novel method for regression that minimizes the statistical dependence between regressors and residuals. The key advantage of this approach to regression is that it does not assume a particular distribution of the noise, i.e., it is non-parametric with respect to the noise distribution. We argue that the proposed regression method is well suited to the task of causal inference in additive noise models. A practical disadvantage is that the resulting optimization problem is generally non-convex and can be difficult to solve. Nevertheless, we report good results on one of the tasks of the NIPS 2008 Causality Challenge, where the goal is to distinguish causes from effects in pairs of statistically dependent variables. In addition, we propose an algorithm for efficiently inferring causal models from observational data for more than two variables. The required number of regressions and independence tests is quadratic in the number of variables, which is a significant improvement over the simple method that tests all possible DAGs.