Node Regression on Latent Position Random Graphs via Local Averaging

• URL: http://arxiv.org/abs/2410.21987v1
• Date: Tue, 29 Oct 2024 12:17:06 GMT
• Title: Node Regression on Latent Position Random Graphs via Local Averaging
• Authors: Martin Gjorgjevski, Nicolas Keriven, Simon Barthelmé, Yohann De Castro,
• Abstract summary: We study the performance of various estimators for node regression. An alternative consists in first estimating the true distances between the latent positions, then injecting these estimated distances into a classical Nadaraya Watson estimator. We show that this method can achieve standard nonparametric rates in certain instances even when the graph neighborhood is too large or too small.
• Score: 10.962094053749093
• License:
• Abstract: Node regression consists in predicting the value of a graph label at a node, given observations at the other nodes. To gain some insight into the performance of various estimators for this task, we perform a theoretical study in a context where the graph is random. Specifically, we assume that the graph is generated by a Latent Position Model, where each node of the graph has a latent position, and the probability that two nodes are connected depend on the distance between the latent positions of the two nodes. In this context, we begin by studying the simplest possible estimator for graph regression, which consists in averaging the value of the label at all neighboring nodes. We show that in Latent Position Models this estimator tends to a Nadaraya Watson estimator in the latent space, and that its rate of convergence is in fact the same. One issue with this standard estimator is that it averages over a region consisting of all neighbors of a node, and that depending on the graph model this may be too much or too little. An alternative consists in first estimating the true distances between the latent positions, then injecting these estimated distances into a classical Nadaraya Watson estimator. This enables averaging in regions either smaller or larger than the typical graph neighborhood. We show that this method can achieve standard nonparametric rates in certain instances even when the graph neighborhood is too large or too small.

Related papers

• Generalization of Geometric Graph Neural Networks [84.01980526069075]
  We study the generalization capabilities of geometric graph neural networks (GNNs) We prove a generalization gap between the optimal empirical risk and the optimal statistical risk of this GNN. The most important observation is that the generalization capability can be realized with one large graph instead of being limited to the size of the graph as in previous results.
  arXiv  Detail & Related papers  (2024-09-08T18:55:57Z)
• Deep Manifold Graph Auto-Encoder for Attributed Graph Embedding [51.75091298017941]
  This paper proposes a novel Deep Manifold (Variational) Graph Auto-Encoder (DMVGAE/DMGAE) for attributed graph data. The proposed method surpasses state-of-the-art baseline algorithms by a significant margin on different downstream tasks across popular datasets.
  arXiv  Detail & Related papers  (2024-01-12T17:57:07Z)
• The Graphical Nadaraya-Watson Estimator on Latent Position Models [0.0]
  We are interested in the quality of the averaging estimator which for an unlabeled node predicts the average of the observations of its labeled neighbors. While the estimator itself is very simple we believe that our results will contribute towards the theoretical understanding of learning on graphs through more sophisticated methods such as Graph Neural Networks.
  arXiv  Detail & Related papers  (2023-03-30T08:56:28Z)
• Unveiling the Sampling Density in Non-Uniform Geometric Graphs [69.93864101024639]
  We consider graphs as geometric graphs: nodes are randomly sampled from an underlying metric space, and any pair of nodes is connected if their distance is less than a specified neighborhood radius. In a social network communities can be modeled as densely sampled areas, and hubs as nodes with larger neighborhood radius. We develop methods to estimate the unknown sampling density in a self-supervised fashion.
  arXiv  Detail & Related papers  (2022-10-15T08:01:08Z)
• Node Copying: A Random Graph Model for Effective Graph Sampling [35.957719744856696]
  We introduce the node copying model for constructing a distribution over graphs. We show the usefulness of the copying model in three tasks. We employ our proposed model to mitigate the effect of adversarial attacks on the graph topology.
  arXiv  Detail & Related papers  (2022-08-04T04:04:49Z)
• Collaborative likelihood-ratio estimation over graphs [55.98760097296213]
  Graph-based Relative Unconstrained Least-squares Importance Fitting (GRULSIF) We develop this idea in a concrete non-parametric method that we call Graph-based Relative Unconstrained Least-squares Importance Fitting (GRULSIF) We derive convergence rates for our collaborative approach that highlights the role played by variables such as the number of available observations per node, the size of the graph, and how accurately the graph structure encodes the similarity between tasks.
  arXiv  Detail & Related papers  (2022-05-28T15:37:03Z)
• Entropic Optimal Transport in Random Graphs [8.7314407902481]
  In graph analysis, a classic task consists in computing similarity measures between (groups of) nodes. We show that it is possible to consistently estimate distances between groups of nodes in the latent space.
  arXiv  Detail & Related papers  (2022-01-11T13:52:34Z)
• Graph Neural Networks with Feature and Structure Aware Random Walk [7.143879014059894]
  We show that in typical heterphilous graphs, the edges may be directed, and whether to treat the edges as is or simply make them undirected greatly affects the performance of the GNN models. We develop a model that adaptively learns the directionality of the graph, and exploits the underlying long-distance correlations between nodes.
  arXiv  Detail & Related papers  (2021-11-19T08:54:21Z)
• Line Graph Neural Networks for Link Prediction [71.00689542259052]
  We consider the graph link prediction task, which is a classic graph analytical problem with many real-world applications. In this formalism, a link prediction problem is converted to a graph classification task. We propose to seek a radically different and novel path by making use of the line graphs in graph theory. In particular, each node in a line graph corresponds to a unique edge in the original graph. Therefore, link prediction problems in the original graph can be equivalently solved as a node classification problem in its corresponding line graph, instead of a graph classification task.
  arXiv  Detail & Related papers  (2020-10-20T05:54:31Z)
• Investigating Extensions to Random Walk Based Graph Embedding [0.3867052484157571]
  We propose a novel extension to random walk based graph embedding, which removes a percentage of least frequent nodes from the walks at different levels. By this removal, we simulate farther distant nodes to reside in the close neighborhood of a node and hence explicitly represent their connection. The results indicate, that extensions to random walk based methods (including our own) improve the predictive performance only slightly - if at all.
  arXiv  Detail & Related papers  (2020-02-17T21:14:02Z)
• 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.