Analytic DAG Constraints for Differentiable DAG Learning

ICLR 2025 Conference Submission5464 Authors

Keywords: DAG, Causal Discovery, Structural Learning

Abstract:

Recovering underlying Directed Acyclic Graph (DAG) structures from observational data presents a formidable challenge due to the combinatorial nature of the DAG-constrained optimization problem. Recently, researchers have identified gradient vanishing as one of the primary obstacles in differentiable DAG learning and have proposed several DAG constraints to mitigate this issue. By developing the necessary theory to establish a connection between analytic functions and DAG constraints, we demonstrate that analytic functions from the set
$\\{f(x) = c_0 + \sum_{i=1}c_ix^i|c_0 \geqslant 0; \forall i > 0, c_i > 0; r = \lim_{i\rightarrow \infty}c_{i}/c_{i+1} > 0\\}$
can be employed to formulate effective DAG constraints. Furthermore, we establish that this set of functions is closed under several functional operators, including differentiation, summation, and multiplication. Consequently, these operators can be leveraged to create novel DAG constraints based on existing ones. Using these properties, we designed a series of DAG constraints and designed an efficient algorithm to evaluate these DAG constraints. Experiments on various settings show that our DAG constraints outperform previous state-of-the-arts approaches.

Primary Area: causal reasoning

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Submission Number: 5464