Graph sparsification is a well-established technique for accelerating graph-based learning algorithms, which uses edge sampling to approximate dense graphs with sparse ones. Because the sparsification error is random and unknown, users must contend with uncertainty about the reliability of downstream computations. Although it is possible for users to obtain conceptual guidance from theoretical error bounds in the literature, such results are typically impractical at a numerical level. Taking an alternative approach, we propose to address these issues from a data-driven perspective by computing empirical error estimates. The proposed error estimates are highly versatile, and we demonstrate this in four use cases: Laplacian matrix approximation, graph cut queries, graph-structured regression, and spectral clustering. Moreover, we provide two theoretical guarantees for the error estimates, and explain why the cost of computing them is manageable in comparison to the overall cost of a typical graph sparsification workflow.
Imitation Learning of MPC with Neural Networks: Error Guarantees and Sparsification
Control and Cyber-Physical Systems Laboratory, Technical University of Darmstadt（达姆施塔特工业大学控制与信息物理系统实验室）；Dept of Chemical & Biomolecular Engineering, University of California, Berkeley（加州大学伯克利分校化学与生物分子工程系）
Theoretical Learning Performance of Graph Neural Networks: The Impact of Jumping Connections and Layer-wise Sparsification
Department of Electrical, Computer, and Systems Engineering（电气、计算机与系统工程系）；Rensselaer Polytechnic Institute（伦塞拉尔理工大学）；Department of Electrical and Systems Engineering（电气与系统工程系）；University of Pennsylvania（宾夕法尼亚大学）
Mask-Encoded Sparsification: Mitigating Biased Gradients in Communication-Efficient Split Learning
Key Laboratory of Water Big Data Technology of Ministry of Water Resources, Hohai University, Nanjing, China（水利部水大数据技术重点实验室，河海大学，南京，中国）；National Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, China（新型软件技术国家实验室，南京大学，南京，中国）；Nanjing University of Aeronautics（南京航空航天大学）
Principle of Relevant Information for Graph Sparsification
UiT - The Arctic University of Norway（特罗姆瑟大学-挪威北极大学）；NEC Laboratories Europe（NEC欧洲实验室）；University of Amsterdam（阿姆斯特丹大学）；Norwegian Computing Center（挪威计算中心）；University of Copenhagen（哥本哈根大学）；University of Florida（佛罗里达大学）
Improving the interpretability of GNN predictions through conformal-based graph sparsification
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；McGill University（麦吉尔大学）；Saarland University（萨尔大学）；Max Planck Institute for Software Systems（马克斯·普朗克软件系统研究所）
