Causal Discovery with Score Matching on Additive Models with Arbitrary Noise
This work addresses a key limitation in causal inference for researchers and practitioners by reducing assumptions, though it is incremental in extending existing additive models.
The paper tackles the problem of causal discovery under restrictive Gaussian noise assumptions in additive non-linear models, showing that these assumptions can lead to edge inversion errors. The authors propose NoGAM, a method that works with arbitrary noise distributions, achieving state-of-the-art performance on synthetic data.
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.