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Truncated Matrix Power Iteration for Differentiable DAG Learning
Zhen Zhang · Ignavier Ng · Dong Gong · Yuhang Liu · Ehsan Abbasnejad · Mingming Gong · Kun Zhang · Javen Qinfeng Shi

Tue Nov 29 09:00 AM -- 11:00 AM (PST) @ Hall J #413
Recovering underlying Directed Acyclic Graph (DAG) structures from observational data is highly challenging due to the combinatorial nature of the DAG-constrained optimization problem. Recently, DAG learning has been cast as a continuous optimization problem by characterizing the DAG constraint as a smooth equality one, generally based on polynomials over adjacency matrices. Existing methods place very small coefficients on high-order polynomial terms for stabilization, since they argue that large coefficients on the higher-order terms are harmful due to numeric exploding. On the contrary, we discover that large coefficients on higher-order terms are beneficial for DAG learning, when the spectral radiuses of the adjacency matrices are small, and that larger coefficients for higher-order terms can approximate the DAG constraints much better than the small counterparts. Based on this, we propose a novel DAG learning method with efficient truncated matrix power iteration to approximate geometric series based DAG constraints. Empirically, our DAG learning method outperforms the previous state-of-the-arts in various settings, often by a factor of $3$ or more in terms of structural Hamming distance.

Author Information

Zhen Zhang (University of Adelaide)
Ignavier Ng (Carnegie Mellon University)
Dong Gong (The University of New South Wales)
Yuhang Liu (The University of Adelaide)
Ehsan Abbasnejad (University of Adelaide)
Mingming Gong (University of Melbourne)
Kun Zhang (CMU & MBZUAI)
Javen Qinfeng Shi (University of Adelaide)

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