Prequential MDL for Causal Structure Learning with Neural Networks

TL;DR

This paper introduces a prequential MDL-based scoring method using neural networks for causal structure learning in Bayesian networks, achieving accurate results even with complex nonlinear relationships without tuning regularizers.

Contribution

It presents a novel application of prequential MDL with neural networks for causal discovery, avoiding the need for sparsity priors or regularizers, and demonstrating robustness to nonlinearities.

Findings

Competitive performance on synthetic data

Effective in recovering true structure with nonlinear relationships

Handles distributional shifts in data

Abstract

Learning the structure of Bayesian networks and causal relationships from observations is a common goal in several areas of science and technology. We show that the prequential minimum description length principle (MDL) can be used to derive a practical scoring function for Bayesian networks when flexible and overparametrized neural networks are used to model the conditional probability distributions between observed variables. MDL represents an embodiment of Occam's Razor and we obtain plausible and parsimonious graph structures without relying on sparsity inducing priors or other regularizers which must be tuned. Empirically we demonstrate competitive results on synthetic and real-world data. The score often recovers the correct structure even in the presence of strongly nonlinear relationships between variables; a scenario were prior approaches struggle and usually fail. Furthermore we discuss how the the prequential score relates to recent work that infers causal structure from the speed of adaptation when the observations come from a source undergoing distributional shift.