Differentiable and Transportable Structure Learning

TL;DR

This paper introduces D-Struct, a differentiable architecture that enhances structure learning of DAGs by ensuring transportability across datasets, improving upon existing methods like NOTEARS.

Contribution

D-Struct recovers transportability in differentiable DAG structure learning through a novel architecture and loss function, compatible with existing differentiable frameworks.

Findings

D-Struct improves edge accuracy across various datasets.

D-Struct reduces structural Hamming distance compared to baseline methods.

D-Struct maintains differentiability, enabling easy integration into existing models.

Abstract

Directed acyclic graphs (DAGs) encode a lot of information about a particular distribution in their structure. However, compute required to infer these structures is typically super-exponential in the number of variables, as inference requires a sweep of a combinatorially large space of potential structures. That is, until recent advances made it possible to search this space using a differentiable metric, drastically reducing search time. While this technique -- named NOTEARS -- is widely considered a seminal work in DAG-discovery, it concedes an important property in favour of differentiability: transportability. To be transportable, the structures discovered on one dataset must apply to another dataset from the same domain. We introduce D-Struct which recovers transportability in the discovered structures through a novel architecture and loss function while remaining fully differentiable. Because D-Struct remains differentiable, our method can be easily adopted in existing differentiable architectures, as was previously done with NOTEARS. In our experiments, we empirically validate D-Struct with respect to edge accuracy and structural Hamming distance in a variety of settings.