Analytic DAG Constraints for Differentiable DAG Learning
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arXiv
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| Main Authors: | , , , , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910892258492416 |
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| author | Zhang, Zhen Ng, Ignavier Gong, Dong Liu, Yuhang Gong, Mingming Huang, Biwei Zhang, Kun Hengel, Anton van den Shi, Javen Qinfeng |
| author_facet | Zhang, Zhen Ng, Ignavier Gong, Dong Liu, Yuhang Gong, Mingming Huang, Biwei Zhang, Kun Hengel, Anton van den Shi, Javen Qinfeng |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_19218 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analytic DAG Constraints for Differentiable DAG Learning Zhang, Zhen Ng, Ignavier Gong, Dong Liu, Yuhang Gong, Mingming Huang, Biwei Zhang, Kun Hengel, Anton van den Shi, Javen Qinfeng Machine Learning 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. |
| title | Analytic DAG Constraints for Differentiable DAG Learning |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2503.19218 |