  Discovering causal structure from purely observational data (i.e., causal
discovery), aiming to identify causal relationships among variables, is a
fundamental task in machine learning. The recent invention of differentiable
score-based DAG learners is a crucial enabler, which reframes the combinatorial
optimization problem into a differentiable optimization with a DAG constraint
over directed graph space. Despite their great success, these cutting-edge DAG
learners incorporate DAG-ness independent score functions to evaluate the
directed graph candidates, lacking in considering graph structure. As a result,
measuring the data fitness alone regardless of DAG-ness inevitably leads to
discovering suboptimal DAGs and model vulnerabilities. Towards this end, we
propose a dynamic causal space for DAG structure learning, coined CASPER, that
integrates the graph structure into the score function as a new measure in the
causal space to faithfully reflect the causal distance between estimated and
ground truth DAG. CASPER revises the learning process as well as enhances the
DAG structure learning via adaptive attention to DAG-ness. Grounded by
empirical visualization, CASPER, as a space, satisfies a series of desired
properties, such as structure awareness and noise robustness. Extensive
experiments on both synthetic and real-world datasets clearly validate the
superiority of our CASPER over the state-of-the-art causal discovery methods in
terms of accuracy and robustness.
