Neuralizing Efficient Higher-order Belief Propagation

• URL: http://arxiv.org/abs/2010.09283v1
• Date: Mon, 19 Oct 2020 07:51:31 GMT
• Title: Neuralizing Efficient Higher-order Belief Propagation
• Authors: Mohammed Haroon Dupty, Wee Sun Lee
• Abstract summary: We propose to combine approaches to learn better node and graph representations. We derive an efficient approximate sum-product loopy belief propagation inference algorithm for higher-order PGMs. Our model indeed captures higher-order information, substantially outperforming state-of-the-art $k$-order graph neural networks in molecular datasets.
• Score: 19.436520792345064
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Graph neural network models have been extensively used to learn node representations for graph structured data in an end-to-end setting. These models often rely on localized first order approximations of spectral graph convolutions and hence are unable to capture higher-order relational information between nodes. Probabilistic Graphical Models form another class of models that provide rich flexibility in incorporating such relational information but are limited by inefficient approximate inference algorithms at higher order. In this paper, we propose to combine these approaches to learn better node and graph representations. First, we derive an efficient approximate sum-product loopy belief propagation inference algorithm for higher-order PGMs. We then embed the message passing updates into a neural network to provide the inductive bias of the inference algorithm in end-to-end learning. This gives us a model that is flexible enough to accommodate domain knowledge while maintaining the computational advantage. We further propose methods for constructing higher-order factors that are conditioned on node and edge features and share parameters wherever necessary. Our experimental evaluation shows that our model indeed captures higher-order information, substantially outperforming state-of-the-art $k$-order graph neural networks in molecular datasets.

Related papers

• Sparse Decomposition of Graph Neural Networks [20.768412002413843]
  We propose an approach to reduce the number of nodes that are included during aggregation. We achieve this through a sparse decomposition, learning to approximate node representations using a weighted sum of linearly transformed features. We demonstrate via extensive experiments that our method outperforms other baselines designed for inference speedup.
  arXiv  Detail & Related papers  (2024-10-25T17:52:16Z)
• Factor Graph Neural Networks [20.211455592922736]
  Graph Neural Networks (GNNs) can learn powerful representations in an end-to-end fashion with great success in many real-world applications. We propose Factor Graph Neural Networks (FGNNs) to effectively capture higher-order relations for inference and learning.
  arXiv  Detail & Related papers  (2023-08-02T00:32:02Z)
• NodeFormer: A Scalable Graph Structure Learning Transformer for Node Classification [70.51126383984555]
  We introduce a novel all-pair message passing scheme for efficiently propagating node signals between arbitrary nodes. The efficient computation is enabled by a kernerlized Gumbel-Softmax operator. Experiments demonstrate the promising efficacy of the method in various tasks including node classification on graphs.
  arXiv  Detail & Related papers  (2023-06-14T09:21:15Z)
• Neural-prior stochastic block model [0.0]
  We propose to model the communities as being determined by the node attributes rather than the opposite. We propose an algorithm, stemming from statistical physics, based on a combination of belief propagation and approximate message passing. The proposed model and algorithm can be used as a benchmark for both theory and algorithms.
  arXiv  Detail & Related papers  (2023-03-17T14:14:54Z)
• Optimal Propagation for Graph Neural Networks [51.08426265813481]
  We propose a bi-level optimization approach for learning the optimal graph structure. We also explore a low-rank approximation model for further reducing the time complexity.
  arXiv  Detail & Related papers  (2022-05-06T03:37:00Z)
• Graph Kernel Neural Networks [53.91024360329517]
  We propose to use graph kernels, i.e. kernel functions that compute an inner product on graphs, to extend the standard convolution operator to the graph domain. This allows us to define an entirely structural model that does not require computing the embedding of the input graph. Our architecture allows to plug-in any type of graph kernels and has the added benefit of providing some interpretability.
  arXiv  Detail & Related papers  (2021-12-14T14:48:08Z)
• Learning to Learn Graph Topologies [27.782971146122218]
  We learn a mapping from node data to the graph structure based on the idea of learning to optimise (L2O) The model is trained in an end-to-end fashion with pairs of node data and graph samples. Experiments on both synthetic and real-world data demonstrate that our model is more efficient than classic iterative algorithms in learning a graph with specific topological properties.
  arXiv  Detail & Related papers  (2021-10-19T08:42:38Z)
• A Unifying Generative Model for Graph Learning Algorithms: Label Propagation, Graph Convolutions, and Combinations [39.8498896531672]
  Semi-supervised learning on graphs is a widely applicable problem in network science and machine learning. We develop a Markov random field model for the data generation process of node attributes. We show that label propagation, a linearized graph convolutional network, and their combination can all be derived as conditional expectations.
  arXiv  Detail & Related papers  (2021-01-19T17:07:08Z)
• Towards Deeper Graph Neural Networks [63.46470695525957]
  Graph convolutions perform neighborhood aggregation and represent one of the most important graph operations. Several recent studies attribute this performance deterioration to the over-smoothing issue. We propose Deep Adaptive Graph Neural Network (DAGNN) to adaptively incorporate information from large receptive fields.
  arXiv  Detail & Related papers  (2020-07-18T01:11:14Z)
• 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)
• Graph Ordering: Towards the Optimal by Learning [69.72656588714155]
  Graph representation learning has achieved a remarkable success in many graph-based applications, such as node classification, prediction, and community detection. However, for some kind of graph applications, such as graph compression and edge partition, it is very hard to reduce them to some graph representation learning tasks. In this paper, we propose to attack the graph ordering problem behind such applications by a novel learning approach.
  arXiv  Detail & Related papers  (2020-01-18T09:14:16Z)

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.