Optimal Exact Recovery in Semi-Supervised Learning: A Study of Spectral Methods and Graph Convolutional Networks

• URL: http://arxiv.org/abs/2412.13754v1
• Date: Wed, 18 Dec 2024 11:44:19 GMT
• Title: Optimal Exact Recovery in Semi-Supervised Learning: A Study of Spectral Methods and Graph Convolutional Networks
• Authors: Hai-Xiao Wang, Zhichao Wang,
• Abstract summary: We tackle the challenge of semi-supervised node classification on the Contextual Block Model (CSBM) dataset. We design an optimal spectral estimator inspired by Principal Component Analysis (PCA) with the training labels and essential data. We also evaluate the efficacy of graph ridge regression and Graph Convolutional Networks (GCN) on this dataset.
• Score: 11.090533263502937
• License:
• Abstract: We delve into the challenge of semi-supervised node classification on the Contextual Stochastic Block Model (CSBM) dataset. Here, nodes from the two-cluster Stochastic Block Model (SBM) are coupled with feature vectors, which are derived from a Gaussian Mixture Model (GMM) that corresponds to their respective node labels. With only a subset of the CSBM node labels accessible for training, our primary objective becomes the accurate classification of the remaining nodes. Venturing into the transductive learning landscape, we, for the first time, pinpoint the information-theoretical threshold for the exact recovery of all test nodes in CSBM. Concurrently, we design an optimal spectral estimator inspired by Principal Component Analysis (PCA) with the training labels and essential data from both the adjacency matrix and feature vectors. We also evaluate the efficacy of graph ridge regression and Graph Convolutional Networks (GCN) on this synthetic dataset. Our findings underscore that graph ridge regression and GCN possess the ability to achieve the information threshold of exact recovery in a manner akin to the optimal estimator when using the optimal weighted self-loops. This highlights the potential role of feature learning in augmenting the proficiency of GCN, especially in the realm of semi-supervised learning.

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)
• Label Deconvolution for Node Representation Learning on Large-scale Attributed Graphs against Learning Bias [75.44877675117749]
  We propose an efficient label regularization technique, namely Label Deconvolution (LD), to alleviate the learning bias by a novel and highly scalable approximation to the inverse mapping of GNNs. Experiments demonstrate LD significantly outperforms state-of-the-art methods on Open Graph datasets Benchmark.
  arXiv  Detail & Related papers  (2023-09-26T13:09:43Z)
• Distributed Learning over Networks with Graph-Attention-Based Personalization [49.90052709285814]
  We propose a graph-based personalized algorithm (GATTA) for distributed deep learning. In particular, the personalized model in each agent is composed of a global part and a node-specific part. By treating each agent as one node in a graph the node-specific parameters as its features, the benefits of the graph attention mechanism can be inherited.
  arXiv  Detail & Related papers  (2023-05-22T13:48:30Z)
• Semantic Graph Neural Network with Multi-measure Learning for Semi-supervised Classification [5.000404730573809]
  Graph Neural Networks (GNNs) have attracted increasing attention in recent years. Recent studies have shown that GNNs are vulnerable to the complex underlying structure of the graph. We propose a novel framework for semi-supervised classification.
  arXiv  Detail & Related papers  (2022-12-04T06:17:11Z)
• Neighborhood Convolutional Network: A New Paradigm of Graph Neural Networks for Node Classification [12.062421384484812]
  Graph Convolutional Network (GCN) decouples neighborhood aggregation and feature transformation in each convolutional layer. In this paper, we propose a new paradigm of GCN, termed Neighborhood Convolutional Network (NCN) In this way, the model could inherit the merit of decoupled GCN for aggregating neighborhood information, at the same time, develop much more powerful feature learning modules.
  arXiv  Detail & Related papers  (2022-11-15T02:02:51Z)
• Interpolation-based Correlation Reduction Network for Semi-Supervised Graph Learning [49.94816548023729]
  We propose a novel graph contrastive learning method, termed Interpolation-based Correlation Reduction Network (ICRN) In our method, we improve the discriminative capability of the latent feature by enlarging the margin of decision boundaries. By combining the two settings, we extract rich supervision information from both the abundant unlabeled nodes and the rare yet valuable labeled nodes for discnative representation learning.
  arXiv  Detail & Related papers  (2022-06-06T14:26:34Z)
• Neural Structured Prediction for Inductive Node Classification [29.908759584092167]
  This paper studies node classification in the inductive setting, aiming to learn a model on labeled training graphs and generalize it to infer node labels on unlabeled test graphs. We present a new approach called the Structured Proxy Network (SPN), which combines the advantages of both worlds.
  arXiv  Detail & Related papers  (2022-04-15T15:50:27Z)
• Infinitely Wide Graph Convolutional Networks: Semi-supervised Learning via Gaussian Processes [144.6048446370369]
  Graph convolutional neural networks(GCNs) have recently demonstrated promising results on graph-based semi-supervised classification. We propose a GP regression model via GCNs(GPGC) for graph-based semi-supervised learning. We conduct extensive experiments to evaluate GPGC and demonstrate that it outperforms other state-of-the-art methods.
  arXiv  Detail & Related papers  (2020-02-26T10:02:32Z)
• Embedding Graph Auto-Encoder for Graph Clustering [90.8576971748142]
  Graph auto-encoder (GAE) models are based on semi-supervised graph convolution networks (GCN) We design a specific GAE-based model for graph clustering to be consistent with the theory, namely Embedding Graph Auto-Encoder (EGAE) EGAE consists of one encoder and dual decoders.
  arXiv  Detail & Related papers  (2020-02-20T09:53:28Z)
• Unifying Graph Convolutional Neural Networks and Label Propagation [73.82013612939507]
  We study the relationship between LPA and GCN in terms of two aspects: feature/label smoothing and feature/label influence. Based on our theoretical analysis, we propose an end-to-end model that unifies GCN and LPA for node classification. Our model can also be seen as learning attention weights based on node labels, which is more task-oriented than existing feature-based attention models.
  arXiv  Detail & Related papers  (2020-02-17T03:23:13Z)

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.