Causal Discovery with Score Matching on Additive Models with Arbitrary Noise

Francesco Montagna, Nicoletta Noceti, Lorenzo Rosasco, Kun Zhang, Francesco Locatello

Keywords: causal discovery, score matching, arbitrary noise distributions

TL;DR: Causal discovery methods often assume Gaussian noise terms. First we show the shortcoming of inference under this assumption; then we propose an algorithm for causal discovery on non linear additive models with generic distribution of the noise.

Abstract: Causal discovery methods are intrinsically constrained by the set of assumptions needed to ensure structure identifiability. Moreover additional restrictions are often imposed in order to simplify the inference task: this is the case for the Gaussian noise assumption on additive non-linear models, which is common to many causal discovery approaches. In this paper we show the shortcomings of inference under this hypothesis, analyzing the risk of edge inversion under violation of Gaussianity of the noise terms. Then, we propose a novel method for inferring the topological ordering of the variables in the causal graph, from data generated according to an additive non-linear model with a generic noise distribution. This leads to NoGAM (Not only Gaussian Additive noise Models), a causal discovery algorithm with a minimal set of assumptions and state of the art performance, experimentally benchmarked on synthetic data.