Differentiable Causal Structure Learning with Identifiability by NOTIME

Jeroen Berrevoets, Jakob Raymaekers, Mihaela van der Schaar, Tim Verdonck, Ruicong Yao

TL;DR: This work provides the first differentiable DAG algorithm with guaranteed identifiability on LiNGAM. The algorithm outperforms NOTEARS and other (scale-invariant) differentiable DAG learners across various settings.

Abstract: The introduction of the NOTEARS algorithm resulted in a wave of research on differentiable Directed Acyclic Graph (DAG) learning. Differentiable DAG learning transforms the combinatorial problem of identifying the DAG underlying a Structural Causal Model (SCM) into a constrained continuous optimization problem. Being differentiable, these problems can be solved using gradient-based tools which allow integration into other differentiable objectives. However, in contrast to classical constrained-based algorithms, the identifiability properties of differentiable algorithms are poorly understood. We illustrate that even in the well-known Linear Non-Gaussian Additive Model (LiNGAM), the current state-of-the-art methods do not identify the true underlying DAG. To address the issue, we propose NOTIME (*Non-combinatorial Optimization of Trace exponential and Independence MEasures*), the first differentiable DAG learning algorithm with *provable* identifiability guarantees under the LiNGAM by building on a measure of (joint) independence. With its identifiability guarantees, NOTIME remains invariant to normalization of the data on a population level, a property lacking in existing methods. NOTIME compares favourably against NOTEARS and other (scale-invariant) differentiable DAG learners, across different noise distributions and normalization procedures. Introducing the first identifiability guarantees to general LiNGAM is an important step towards practical adoption of differentiable DAG learners.

Submission Number: 1118