2022/08/30 by Zhen Zhang, Ignavier Ng, Zhang, Zhen +13 · 2 citations
Chemistry · Computer Science · Engineering · #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #Image Retrieval and Classification Techniques #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Molecular spectroscopy and chirality #Remote-Sensing Image Classification
paper · pdf · doi:10.48550/arxiv.2208.14571
openalex publication_date 2022/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.