Generalization of graph network inferences in higher-order graphical models

• URL: http://arxiv.org/abs/2107.05729v2
• Date: Wed, 3 May 2023 03:25:53 GMT
• Title: Generalization of graph network inferences in higher-order graphical models
• Authors: Yicheng Fei, Xaq Pitkow
• Abstract summary: Probabilistic graphical models provide a powerful tool to describe complex statistical structure. inferences such as marginalization are intractable for general graphs. We define the Recurrent Factor Graph Neural Network (RF-GNN) to achieve fast approximate inference on graphical models that involve many-variable interactions.
• Score: 5.33024001730262
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: Probabilistic graphical models provide a powerful tool to describe complex statistical structure, with many real-world applications in science and engineering from controlling robotic arms to understanding neuronal computations. A major challenge for these graphical models is that inferences such as marginalization are intractable for general graphs. These inferences are often approximated by a distributed message-passing algorithm such as Belief Propagation, which does not always perform well on graphs with cycles, nor can it always be easily specified for complex continuous probability distributions. Such difficulties arise frequently in expressive graphical models that include intractable higher-order interactions. In this paper we define the Recurrent Factor Graph Neural Network (RF-GNN) to achieve fast approximate inference on graphical models that involve many-variable interactions. Experimental results on several families of graphical models demonstrate the out-of-distribution generalization capability of our method to different sized graphs, and indicate the domain in which our method outperforms Belief Propagation (BP). Moreover, we test the RF-GNN on a real-world Low-Density Parity-Check dataset as a benchmark along with other baseline models including BP variants and other GNN methods. Overall we find that RF-GNNs outperform other methods under high noise levels.

Related papers

• Generalization of Graph Neural Networks is Robust to Model Mismatch [84.01980526069075]
  Graph neural networks (GNNs) have demonstrated their effectiveness in various tasks supported by their generalization capabilities. In this paper, we examine GNNs that operate on geometric graphs generated from manifold models. Our analysis reveals the robustness of the GNN generalization in the presence of such model mismatch.
  arXiv  Detail & Related papers  (2024-08-25T16:00:44Z)
• Almost Surely Asymptotically Constant Graph Neural Networks [7.339728196535312]
  We show that the output converges to a constant function, which upper-bounds what these classifiers can uniformly express. Results apply to a broad class of random graph models. We empirically validate these findings, observing that the convergence phenomenon appears not only on random graphs but also on some real-world graphs.
  arXiv  Detail & Related papers  (2024-03-06T17:40:26Z)
• Advective Diffusion Transformers for Topological Generalization in Graph Learning [69.2894350228753]
  We show how graph diffusion equations extrapolate and generalize in the presence of varying graph topologies. We propose a novel graph encoder backbone, Advective Diffusion Transformer (ADiT), inspired by advective graph diffusion equations.
  arXiv  Detail & Related papers  (2023-10-10T08:40:47Z)
• Relation Embedding based Graph Neural Networks for Handling Heterogeneous Graph [58.99478502486377]
  We propose a simple yet efficient framework to make the homogeneous GNNs have adequate ability to handle heterogeneous graphs. Specifically, we propose Relation Embedding based Graph Neural Networks (RE-GNNs), which employ only one parameter per relation to embed the importance of edge type relations and self-loop connections.
  arXiv  Detail & Related papers  (2022-09-23T05:24:18Z)
• Towards Better Generalization with Flexible Representation of Multi-Module Graph Neural Networks [0.27195102129094995]
  We use a random graph generator to investigate how the graph size and structural properties affect the predictive performance of GNNs. We present specific evidence that the average node degree is a key feature in determining whether GNNs can generalize to unseen graphs. We propose a multi- module GNN framework that allows the network to adapt flexibly to new graphs by generalizing a single canonical nonlinear transformation over aggregated inputs.
  arXiv  Detail & Related papers  (2022-09-14T12:13:59Z)
• Graph Generative Model for Benchmarking Graph Neural Networks [73.11514658000547]
  We introduce a novel graph generative model that learns and reproduces the distribution of real-world graphs in a privacy-controlled way. Our model can successfully generate privacy-controlled, synthetic substitutes of large-scale real-world graphs that can be effectively used to benchmark GNN models.
  arXiv  Detail & Related papers  (2022-07-10T06:42:02Z)
• OOD-GNN: Out-of-Distribution Generalized Graph Neural Network [73.67049248445277]
  Graph neural networks (GNNs) have achieved impressive performance when testing and training graph data come from identical distribution. Existing GNNs lack out-of-distribution generalization abilities so that their performance substantially degrades when there exist distribution shifts between testing and training graph data. We propose an out-of-distribution generalized graph neural network (OOD-GNN) for achieving satisfactory performance on unseen testing graphs that have different distributions with training graphs.
  arXiv  Detail & Related papers  (2021-12-07T16:29:10Z)
• Crime Prediction with Graph Neural Networks and Multivariate Normal Distributions [18.640610803366876]
  We tackle the sparsity problem in high resolution by leveraging the flexible structure of graph convolutional networks (GCNs) We build our model with Graph Convolutional Gated Recurrent Units (Graph-ConvGRU) to learn spatial, temporal, and categorical relations. We show that our model is not only generative but also precise.
  arXiv  Detail & Related papers  (2021-11-29T17:37:01Z)
• Block-Approximated Exponential Random Graphs [77.4792558024487]
  An important challenge in the field of exponential random graphs (ERGs) is the fitting of non-trivial ERGs on large graphs. We propose an approximative framework to such non-trivial ERGs that result in dyadic independence (i.e., edge independent) distributions. Our methods are scalable to sparse graphs consisting of millions of nodes.
  arXiv  Detail & Related papers  (2020-02-14T11:42:16Z)

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.