Causal Discovery with Score Matching on Additive Models with Arbitrary Noise

TL;DR

This paper introduces NoGAM, a causal discovery method that infers variable orderings in additive models with arbitrary noise, overcoming limitations of Gaussian noise assumptions and demonstrating strong performance on synthetic data.

Contribution

The paper proposes NoGAM, a novel causal discovery algorithm that operates under minimal assumptions and handles arbitrary noise distributions, improving over Gaussian-based methods.

Findings

NoGAM accurately infers causal orderings with arbitrary noise.

It outperforms Gaussian-based methods on synthetic benchmarks.

The approach is robust to violations of Gaussian noise assumptions.

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.