Stable Differentiable Causal Discovery
Achille Nazaret Justin Hong Elham Azizi David Blei
Inferring causal relationships as directed acyclic graphs (DAGs) is an
important but challenging problem. Differentiable Causal Discovery (DCD) is a
promising approach to this problem, framing the search as a continuous
optimization. But existing DCD methods are numerically unstable, with poor
performance beyond tens of variables. In this paper, we propose Stable
Differentiable Causal Discovery (SDCD), a new method that improves previous DCD
methods in two ways: (1) It employs an alternative constraint for acyclicity;
this constraint is more stable, both theoretically and empirically, and fast to
compute. (2) It uses a training procedure tailored for sparse causal graphs,
which are common in real-world scenarios. We first derive SDCD and prove its
stability and correctness. We then evaluate it with both observational and
interventional data and on both small-scale and large-scale settings. We find
that SDCD outperforms existing methods in both convergence speed and accuracy
and can scale to thousands of variables.