Differentiable and Transportable Structure Learning
This work addresses the need for transportable DAG structures in causal inference and machine learning, offering an incremental improvement over existing differentiable methods.
The paper tackles the problem of learning directed acyclic graphs (DAGs) that are transportable across datasets, addressing a limitation in the NOTEARS method which sacrifices transportability for differentiability. The result is D-Struct, a novel architecture and loss function that recovers transportability while remaining differentiable, with empirical validation showing improvements in edge accuracy and structural Hamming distance.
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.