Optimization and Generalization Analysis of Transduction through Gradient Boosting and Application to Multi-scale Graph Neural Networks

• URL: http://arxiv.org/abs/2006.08550v3
• Date: Wed, 6 Jan 2021 14:17:46 GMT
• Title: Optimization and Generalization Analysis of Transduction through Gradient Boosting and Application to Multi-scale Graph Neural Networks
• Authors: Kenta Oono, Taiji Suzuki
• Abstract summary: It is known that the current graph neural networks (GNNs) are difficult to make themselves deep due to the problem known as over-smoothing. Multi-scale GNNs are a promising approach for mitigating the over-smoothing problem. We derive the optimization and generalization guarantees of transductive learning algorithms that include multi-scale GNNs.
• Score: 60.22494363676747
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: It is known that the current graph neural networks (GNNs) are difficult to make themselves deep due to the problem known as over-smoothing. Multi-scale GNNs are a promising approach for mitigating the over-smoothing problem. However, there is little explanation of why it works empirically from the viewpoint of learning theory. In this study, we derive the optimization and generalization guarantees of transductive learning algorithms that include multi-scale GNNs. Using the boosting theory, we prove the convergence of the training error under weak learning-type conditions. By combining it with generalization gap bounds in terms of transductive Rademacher complexity, we show that a test error bound of a specific type of multi-scale GNNs that decreases corresponding to the number of node aggregations under some conditions. Our results offer theoretical explanations for the effectiveness of the multi-scale structure against the over-smoothing problem. We apply boosting algorithms to the training of multi-scale GNNs for real-world node prediction tasks. We confirm that its performance is comparable to existing GNNs, and the practical behaviors are consistent with theoretical observations. Code is available at https://github.com/delta2323/GB-GNN.

Related papers

• A Manifold Perspective on the Statistical Generalization of Graph Neural Networks [84.01980526069075]
  We take a manifold perspective to establish the statistical generalization theory of GNNs on graphs sampled from a manifold in the spectral domain. We prove that the generalization bounds of GNNs decrease linearly with the size of the graphs in the logarithmic scale, and increase linearly with the spectral continuity constants of the filter functions.
  arXiv  Detail & Related papers  (2024-06-07T19:25:02Z)
• Learning to Reweight for Graph Neural Network [63.978102332612906]
  Graph Neural Networks (GNNs) show promising results for graph tasks. Existing GNNs' generalization ability will degrade when there exist distribution shifts between testing and training graph data. We propose a novel nonlinear graph decorrelation method, which can substantially improve the out-of-distribution generalization ability.
  arXiv  Detail & Related papers  (2023-12-19T12:25:10Z)
• How Graph Neural Networks Learn: Lessons from Training Dynamics [80.41778059014393]
  We study the training dynamics in function space of graph neural networks (GNNs) We find that the gradient descent optimization of GNNs implicitly leverages the graph structure to update the learned function. This finding offers new interpretable insights into when and why the learned GNN functions generalize.
  arXiv  Detail & Related papers  (2023-10-08T10:19:56Z)
• Empowering Counterfactual Reasoning over Graph Neural Networks through Inductivity [7.094238868711952]
  Graph neural networks (GNNs) have various practical applications, such as drug discovery, recommendation engines, and chip design. Counterfactual reasoning is used to make minimal changes to the input graph of a GNN in order to alter its prediction.
  arXiv  Detail & Related papers  (2023-06-07T23:40:18Z)
• Optimization of Graph Neural Networks: Implicit Acceleration by Skip Connections and More Depth [57.10183643449905]
  Graph Neural Networks (GNNs) have been studied from the lens of expressive power and generalization. We study the dynamics of GNNs by studying deep skip optimization. Our results provide first theoretical support for the success of GNNs.
  arXiv  Detail & Related papers  (2021-05-10T17:59:01Z)
• Learning Graph Neural Networks with Approximate Gradient Descent [24.49427608361397]
  Two types of graph neural networks (GNNs) are investigated, depending on whether labels are attached to nodes or graphs. A comprehensive framework for designing and analyzing convergence of GNN training algorithms is developed. The proposed algorithm guarantees a linear convergence rate to the underlying true parameters of GNNs.
  arXiv  Detail & Related papers  (2020-12-07T02:54:48Z)
• Expressive Power of Invariant and Equivariant Graph Neural Networks [10.419350129060598]
  We show that Folklore Graph Neural Networks (FGNN) are the most expressive architectures proposed so far for a given tensor order. FGNNs are able to learn how to solve the problem, leading to much better average performances than existing algorithms.
  arXiv  Detail & Related papers  (2020-06-28T16:35:45Z)
• Fast Learning of Graph Neural Networks with Guaranteed Generalizability: One-hidden-layer Case [93.37576644429578]
  Graph neural networks (GNNs) have made great progress recently on learning from graph-structured data in practice. We provide a theoretically-grounded generalizability analysis of GNNs with one hidden layer for both regression and binary classification problems.
  arXiv  Detail & Related papers  (2020-06-25T00:45:52Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.