Theoretical and Computational Guarantees of Mean Field Variational Inference for Community Detection
Theoretical and Computational Guarantees of Mean Field Variational Inference for Community Detection
复制标题
用于社区检测的平均场变分推理的理论和计算保证
DOI：
10.1214/19-aos1898
复制
发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Harrison H. Zhou
中科院分区：
文献类型：
--
作者：
A. Zhang;Harrison H. Zhou
均值场变分贝叶斯方法在统计学和机器学习中越来越受欢迎。其迭代坐标上升变分推理算法已广泛应用于大规模贝叶斯推理。参见Blei et al.（2017）最近的全面综述。尽管平均场方法很受欢迎，但基本的理论依据却很少。据我们所知，迭代算法从来没有研究过任何高维和复杂的模型。本文研究了随机块模型下的平均场社区检测方法。对于一个迭代的批坐标上升变分推理算法，我们证明了它有一个线性收敛速度和收敛到极小极大率内$\log n$迭代。这补充了Bickel等人的结果。（2013）研究了平均场变分贝叶斯的全局最小值，并获得了全局模型参数的渐近正态估计。此外，我们得到了类似的最优性结果吉布斯抽样和迭代过程来计算最大似然估计，这可以是独立的兴趣。
The mean field variational Bayes method is becoming increasingly popular in statistics and machine learning. Its iterative Coordinate Ascent Variational Inference algorithm has been widely applied to large scale Bayesian inference. See Blei et al. (2017) for a recent comprehensive review. Despite the popularity of the mean field method there exist remarkably little fundamental theoretical justifications. To the best of our knowledge, the iterative algorithm has never been investigated for any high dimensional and complex model. In this paper, we study the mean field method for community detection under the Stochastic Block Model. For an iterative Batch Coordinate Ascent Variational Inference algorithm, we show that it has a linear convergence rate and converges to the minimax rate within $\log n$ iterations. This complements the results of Bickel et al. (2013) which studied the global minimum of the mean field variational Bayes and obtained asymptotic normal estimation of global model parameters. In addition, we obtain similar optimality results for Gibbs sampling and an iterative procedure to calculate maximum likelihood estimation, which can be of independent interest.
块模型 SDP 的指数错误率：超越 Grothendieck 不等式
影响因子：
2.5
作者：
Fei, Yingjie;Chen, Yudong
通讯作者：
Chen, Yudong
影响因子：
8.6
作者：
Hofman, Jake M.;Wiggins, Chris H.
通讯作者：
Wiggins, Chris H.