Prequential MDL for Causal Structure Learning with Neural Networks
This work addresses the challenge of causal structure learning for scientists and technologists, offering a method that avoids tuning regularizers, but it appears incremental as it builds on existing MDL principles with neural networks.
The paper tackles the problem of learning Bayesian network and causal structures from observational data by introducing a scoring function based on the prequential minimum description length principle, using neural networks for conditional probability distributions. It demonstrates competitive results on synthetic and real-world data, often recovering correct structures even with strongly nonlinear relationships where prior methods struggle.
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.