Differentiable Causal Structure Learning with Identifiability by NOTIME

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 (\emph{Non-combinatorial Optimization of Trace exponential and Independence MEasures}), the first differentiable DAG learning algorithm with \emph{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.