Stable Differentiable Causal Discovery

Mathematically, a set of causal relations can be represented with a directed acyclic graph (DAG) where nodes are variables, and directed edges indicate direct causal effects. The goal of causal discovery is to recover the graph from the observed data. The data can either be interventional, where some variables were purposely manipulated, or purely observational, where there has been no manipulation. The challenge of causal discovery is the search for the true DAGs is NP-hard. Exact methods are intractable, even for modest numbers of variables [Chi96]. Yet datasets in fields like biology routinely involve thousands of variables [Dix+16]. To address this problem, Zheng et al. [Zhe+18] introduced Differentiable Causal Discovery (DCD), which formulates the DAG search as a continuous optimization over the space of all graph adjacency matrices. An essential element of this strategy is an acyclicity constraint, in the form of a penalty, that guides an otherwise unconstrained search toward acyclic graphs.