当前位置: X-MOL 学术Mach. Learn. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Smoothing graphons for modelling exchangeable relational data
Machine Learning ( IF 7.5 ) Pub Date : 2021-08-24 , DOI: 10.1007/s10994-021-06046-y
Yaqiong Li 1 , Ling Chen 1 , Xuhui Fan 2 , Scott A. Sisson 2 , Bin Li 3
Affiliation  

Modelling exchangeable relational data can be described appropriately in graphon theory. Most Bayesian methods for modelling exchangeable relational data can be attributed to this framework by exploiting different forms of graphons. However, the graphons adopted by existing Bayesian methods are either piecewise-constant functions, which are insufficiently flexible for accurate modelling of the relational data, or are complicated continuous functions, which incur heavy computational costs for inference. In this work, we overcome these two shortcomings by smoothing piecewise-constant graphons, which permits continuous intensity values for describing relations, without impractically increasing computational costs. In particular, we focus on the Bayesian Stochastic Block Model (SBM) and demonstrate how to adapt the piecewise-constant SBM graphon to the smoothed version. We first propose the Integrated Smoothing Graphon (ISG) which introduces one smoothing parameter to the SBM graphon to generate continuous relational intensity values. Then, we further develop the Latent Feature Smoothing Graphon (LFSG), which improves the ISG, by introducing auxiliary hidden labels to decompose the calculation of the ISG intensity and enable efficient inference. Experimental results on real-world data sets validate the advantages of applying smoothing strategies to the Stochastic Block Model, demonstrating that smoothing graphons can greatly improve AUC and precision for link prediction without increasing computational complexity.



中文翻译:

用于建模可交换关系数据的平滑图形

建模可交换的关系数据可以在图论中适当地描述. 大多数用于建模可交换关系数据的贝叶斯方法都可以通过利用不同形式的图形来归因于该框架。然而,现有贝叶斯方法采用的图子要么是分段常数函数,对于关系数据的准确建模不够灵活,要么是复杂的连续函数,这会导致大量的推理计算成本。在这项工作中,我们通过平滑分段常数图形来克服这两个缺点,这允许用于描述关系的连续强度值,而不会不切实际地增加计算成本。特别是,我们专注于贝叶斯随机块模型 (SBM) 并演示如何将分段常数 SBM 图适应平滑版本。我们首先提出了集成平滑图形(ISG),它向 SBM 图形引入了一个平滑参数以生成连续的关系强度值。然后,我们进一步开发了潜在特征平滑图 (LFSG),通过引入辅助隐藏标签来分解 ISG 强度的计算并实现高效推理,从而改进 ISG。在真实世界数据集上的实验结果验证了将平滑策略应用于随机块模型的优势,表明平滑图形可以在不增加计算复杂度的情况下极大地提高 AUC 和链路预测的精度。通过引入辅助隐藏标签来分解 ISG 强度的计算并实现高效推理。在真实世界数据集上的实验结果验证了将平滑策略应用于随机块模型的优势,表明平滑图形可以在不增加计算复杂度的情况下极大地提高 AUC 和链路预测的精度。通过引入辅助隐藏标签来分解 ISG 强度的计算并实现高效推理。在真实世界数据集上的实验结果验证了将平滑策略应用于随机块模型的优势,表明平滑图形可以在不增加计算复杂度的情况下极大地提高 AUC 和链路预测的精度。

更新日期:2021-08-25
down
wechat
bug