Identifiable Nonlinear Differentiable Causal Discovery via Independence and Adaptive Group Sparsity

Differentiable approaches to causal discovery have shown promise in learning DAG structures via continuous optimization, but their theoretical guarantees are largely restricted to models with homoscedastic noise or known noise distribution. In particular, existing methods based on mean squared error fail to identify the true DAG when noise distributions are non-Gaussian and vary in scale. In this paper, we address this gap in nonlinear additive noise models (ANMs) with arbitrary noise. Our approach extends NOTIME (Berrevoets et al. 2025) which minimizes an independence criterion among the residuals. We show that the global minimizer of the independence criterion corresponds to the true underlying DAG up to additional constant edges in general ANMs. To recover the exact structure, we introduce an adaptive group lasso penalty that regularizes entire columns of the first-layer weight matrix of an MLP, enabling the selective pruning of constant edges in a functionally meaningful way. Empirically, our method achieves effective and stable performance across diverse noise types and variances, outperforming prior methods that lack identifiability guarantees in this setting.

How can we discover what causes what when we cannot run experiments? This question appears in many areas, such as biology, medicine, economics, and public policy. For example, scientists may want to know which molecules influence each other inside a cell, but directly testing every possible interaction can be expensive or impossible. Our work develops a new machine learning method for learning cause-and-effect diagrams from observational data. The key idea is simple: after accounting for the right causes, what remains should look like independent background noise. We use this idea to guide the learning algorithm, rather than relying only on prediction accuracy. We also add tools that help the algorithm start from a reasonable guess and remove unnecessary connections. This makes the method more reliable when relationships are nonlinear and when different variables have very different noise levels. It can help researchers generate better causal hypotheses from data, while still requiring careful scientific validation.