贝叶斯对指数随机图模型的分析使用静态梯度马尔科夫链蒙特卡洛.
1Department of Statistics, Purdue University, West Lafayette, IN 47907, USA.
随机梯度兰杰文动力学 (SGLD) 提供了一个可扩展的解决方案,用于分析由指数随机图模型 (ERGM) 建模的大型社交网络. 这种方法有效地从复杂的后面分布中取样,克服统计研究中的计算挑战.
科学领域:
- 统计建模 统计建模
- 网络分析 网络分析
- 计算统计的计算统计.
背景情况:
- 指数随机图模型 (ERGM) 广泛用于社交网络分析.
- ERGM具有难以处理的概率函数,这给后续采样带来了重大挑战.
- 使用高维ERGM分析大规模网络仍然是一个计算密集的问题.
研究的目的:
- 评估随机梯度朗格温动力学 (SGLD) 在ERGM后端采样中的性能.
- 开发一个可扩展的算法来分析大型和复杂的社交网络.
- 为了解决从难以解决的ERGM概率抽样的长期问题.
主要方法:
- 随机梯度朗格温动力学 (SGLD) 的应用,也被称为杂的朗格温蒙特卡罗.
- 在每个代中使用短内马尔科夫链计算随机梯度.
- 在网络规模不断增长的背景下,对SGLD的收特性进行理论分析.
主要成果:
- 对于大型网络和代数,SGLD在2-Wasserstein距离中证明了对真后部的收.
- 无论内部马尔科夫链的长度如何,都会实现趋同,前提是模型大小与网络大小相比缓慢增长.
- 拟议的SGLD方法为高维ERGM分析提供了一个可扩展的解决方案.
结论:
- SGLD提供了一种有效且可扩展的方法,用于使用ERGM分析大规模的社交网络.
- 该算法克服了与难以处理的概率函数相关的计算障碍.
- 这项研究为统计网络分析提供了一个实用的工具.
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