Curvature Filtrations for Graph Generative Model Evaluation

• URL: http://arxiv.org/abs/2301.12906v3
• Date: Thu, 26 Oct 2023 10:18:20 GMT
• Title: Curvature Filtrations for Graph Generative Model Evaluation
• Abstract summary: Graph generative model evaluation requires understanding differences between graphs on the distributional level. Curvature constitutes one such property that has recently proved its utility in characterising graphs. We combine graph curvature descriptors with emerging methods from topological data analysis to obtain robust, expressive descriptors for evaluating graph generative models.
• Score: 11.55292147747249
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Graph generative model evaluation necessitates understanding differences between graphs on the distributional level. This entails being able to harness salient attributes of graphs in an efficient manner. Curvature constitutes one such property that has recently proved its utility in characterising graphs. Its expressive properties, stability, and practical utility in model evaluation remain largely unexplored, however. We combine graph curvature descriptors with emerging methods from topological data analysis to obtain robust, expressive descriptors for evaluating graph generative models.

Related papers

• $α$-Graph: Attention-Infused Normalizing Flow Approach to Tractable Graph Modeling [24.30806125547819]
  We introduce a novel Attention-based Normalizing Flow-based ApproachfootnoteOur implementation and models will be released publicly for research (ANFA or $$)<n>In particular, we propose a new Unconditional Graph Normalizing Flow with an Invertible Attention Mechanism to capture the complex relational structure of graph data.<n>We show that our Conditional Graph Normalizing Flows behave similarly to Unconditional Graph Normalizing Flows, enhancing expressiveness while maintaining training stability and efficiency.
  arXiv  Detail & Related papers  (2026-09-07T20:40:16Z)
• DiPhon: Diffusion on Graphons for Scalable Graph Generation [100.75398811422308]
  Diffusion models represent a leading paradigm for graph generation, with notable impact in domains such as molecular design.<n>We propose DiPhon, a discretized graph-level process that mimics these dynamics on finite graphs.<n>We prove that DiPhon matches exactly the first moment of the marginal distributions induced by the continuous graphon process, and approximates the second moment up to a closed-form discrepancy.
  arXiv  Detail & Related papers  (2026-07-08T10:15:17Z)
• TinyGraphEstimator: Adapting Lightweight Language Models for Graph Structure Inference [0.48302896549293584]
  This paper investigates whether compact transformer-based language models can infer graph-theoretic parameters directly from graph representations.<n>We introduce the TinyGraphEstimator dataset - a collection of connected graphs generated from multiple random graph models.<n>We evaluate several small open models on their ability to predict key graph parameters such as density, clustering, and chromatic number.
  arXiv  Detail & Related papers  (2025-10-09T20:47:07Z)
• TopER: Topological Embeddings in Graph Representation Learning [8.052380377159398]
  Topological Evolution Rate (TopER) is a low-dimensional embedding approach grounded in topological data analysis. TopER simplifies a key topological approach, Persistent Homology, by calculating the evolution rate of graph substructures. Our models achieve or surpass state-of-the-art results across molecular, biological, and social network datasets in tasks such as classification, clustering, and visualization.
  arXiv  Detail & Related papers  (2024-10-02T17:31:33Z)
• GraphRCG: Self-Conditioned Graph Generation [78.69810678803248]
  We propose a novel self-conditioned graph generation framework designed to explicitly model graph distributions. Our framework demonstrates superior performance over existing state-of-the-art graph generation methods in terms of graph quality and fidelity to training data.
  arXiv  Detail & Related papers  (2024-03-02T02:28:20Z)
• Fine-grained Graph Rationalization [51.293401030058085]
  We propose fine-grained graph rationalization (FIG) for graph machine learning. Our idea is driven by the self-attention mechanism, which provides rich interactions between input nodes. Our experiments involve 7 real-world datasets, and the proposed FIG shows significant performance advantages compared to 13 baseline methods.
  arXiv  Detail & Related papers  (2023-12-13T02:56:26Z)
• GraphMaker: Can Diffusion Models Generate Large Attributed Graphs? [7.330479039715941]
  Large-scale graphs with node attributes are increasingly common in various real-world applications. Traditional graph generation methods are limited in their capacity to handle these complex structures. This paper introduces a novel diffusion model, GraphMaker, specifically designed for generating large attributed graphs.
  arXiv  Detail & Related papers  (2023-10-20T22:12:46Z)
• An Accurate Graph Generative Model with Tunable Features [0.8192907805418583]
  We propose a method to improve the accuracy of GraphTune by adding a new mechanism to feed back errors of graph features. Experiments on a real-world graph dataset showed that the features in the generated graphs are accurately tuned compared with conventional models.
  arXiv  Detail & Related papers  (2023-09-03T12:34:15Z)
• Bures-Wasserstein Means of Graphs [60.42414991820453]
  We propose a novel framework for defining a graph mean via embeddings in the space of smooth graph signal distributions. By finding a mean in this embedding space, we can recover a mean graph that preserves structural information. We establish the existence and uniqueness of the novel graph mean, and provide an iterative algorithm for computing it.
  arXiv  Detail & Related papers  (2023-05-31T11:04:53Z)
• Heterogeneous Graph Neural Networks using Self-supervised Reciprocally Contrastive Learning [102.9138736545956]
  Heterogeneous graph neural network (HGNN) is a very popular technique for the modeling and analysis of heterogeneous graphs. We develop for the first time a novel and robust heterogeneous graph contrastive learning approach, namely HGCL, which introduces two views on respective guidance of node attributes and graph topologies. In this new approach, we adopt distinct but most suitable attribute and topology fusion mechanisms in the two views, which are conducive to mining relevant information in attributes and topologies separately.
  arXiv  Detail & Related papers  (2022-04-30T12:57:02Z)
• GraphDCA -- a Framework for Node Distribution Comparison in Real and Synthetic Graphs [72.51835626235368]
  We argue that when comparing two graphs, the distribution of node structural features is more informative than global graph statistics. We present GraphDCA - a framework for evaluating similarity between graphs based on the alignment of their respective node representation sets.
  arXiv  Detail & Related papers  (2022-02-08T14:19:19Z)
• GraphSVX: Shapley Value Explanations for Graph Neural Networks [81.83769974301995]
  Graph Neural Networks (GNNs) achieve significant performance for various learning tasks on geometric data. In this paper, we propose a unified framework satisfied by most existing GNN explainers. We introduce GraphSVX, a post hoc local model-agnostic explanation method specifically designed for GNNs.
  arXiv  Detail & Related papers  (2021-04-18T10:40:37Z)
• A Tunable Model for Graph Generation Using LSTM and Conditional VAE [1.399948157377307]
  We propose a generative model that can tune specific features, while learning structural features of a graph from data. With a dataset of graphs with various features generated by a model, we confirm that our model can generate a graph with specific features.
  arXiv  Detail & Related papers  (2021-04-15T06:47:14Z)
• Certified Robustness of Graph Classification against Topology Attack with Randomized Smoothing [22.16111584447466]
  Graph-based machine learning models are vulnerable to adversarial perturbations due to the non i.i.d nature of graph data. We build a smoothed graph classification model with certified robustness guarantee. We also evaluate the effectiveness of our approach under graph convolutional network (GCN) based multi-class graph classification model.
  arXiv  Detail & Related papers  (2020-09-12T22:18:54Z)
• Graph Pooling with Node Proximity for Hierarchical Representation Learning [80.62181998314547]
  We propose a novel graph pooling strategy that leverages node proximity to improve the hierarchical representation learning of graph data with their multi-hop topology. Results show that the proposed graph pooling strategy is able to achieve state-of-the-art performance on a collection of public graph classification benchmark datasets.
  arXiv  Detail & Related papers  (2020-06-19T13:09:44Z)

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.