Differentiable and transportable structure learning

Jeroen Berrevoets, Nabeel Seedat, Fergus Imrie, Mihaela van der Schaar

Keywords: graph learning

TL;DR: We introduce an architecture and loss to encourage transportability in gradient-based graph learning methods. Before our method, gradient-based approaches were not transportable.

Abstract: Directed acyclic graphs (DAGs) encode a lot of information about a particular distribution in its 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. In our paper, we introduce D-Struct which recovers transportability in the discovered structures through a novel architecture and loss function, while remaining completely 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.

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