Analytic DAG Constraints for Differentiable DAG Learning

• URL: http://arxiv.org/abs/2503.19218v1
• Date: Mon, 24 Mar 2025 23:51:35 GMT
• Title: Analytic DAG Constraints for Differentiable DAG Learning
• Authors: Zhen Zhang, Ignavier Ng, Dong Gong, Yuhang Liu, Mingming Gong, Biwei Huang, Kun Zhang, Anton van den Hengel, Javen Qinfeng Shi,
• Abstract summary: We develop a theory to establish a connection between analytic functions and DAG constraints.<n>We show that analytic functions from the set $f(x) = c_0 + sum_i=1inftyc_ixi | forall i > 0, c_i > 0; r = lim_irightarrow inftyc_i/c_i+1 > 0$ can be employed to formulate effective DAG constraints.
• Score: 83.93320658222717
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Recovering the underlying Directed Acyclic Graph (DAG) structures from observational data presents a formidable challenge, partly 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 $\{f(x) = c_0 + \sum_{i=1}^{\infty}c_ix^i | \forall i > 0, c_i > 0; r = \lim_{i\rightarrow \infty}c_{i}/c_{i+1} > 0\}$ 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 design a series of DAG constraints and develop an efficient algorithm to evaluate them. Experiments in various settings demonstrate that our DAG constraints outperform previous state-of-the-art comparators. Our implementation is available at https://github.com/zzhang1987/AnalyticDAGLearning.

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