Change Point Estimation in a Dynamic Stochastic Block Model
Change Point Estimation in a Dynamic Stochastic Block Model
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发表时间：
2018-12
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通讯作者：
M. Bhattacharjee;M. Banerjee;G. Michailidis
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作者：
M. Bhattacharjee;M. Banerjee;G. Michailidis
我们考虑估计动态随机块模型中单个变更点位置的问题。我们提出了两种估计变更点以及模型参数的方法。第一个采用了最小二乘标准函数，并考虑了随机块模型的完整结构，并在每个时间点进行评估。因此，作为一个中间步骤，它需要根据每个时间点的聚类算法来估算社区结构。第二种方法包括以下两个步骤：在第一个步骤中，在每个时间点都使用和评估一个最小二乘函数，但忽略了社区结构，只是考虑了一个随机图生成机制，该机制显示出变化点。一旦确定了变更点，在第二步中，将其与聚类算法一起使用之前和之后的所有网络数据，以获取相应的社区结构，然后估算生成的随机块模型参数。说明了这两种方法之间的比较。此外，对于两种方法在其各自的可识别性和某些其他规律性条件下的方法，我们都建立了收敛速度并得出变化点估计器的渐近分布。结果在综合数据上进行了说明。
We consider the problem of estimating the location of a single change point in a dynamic stochastic block model. We propose two methods of estimating the change point, together with the model parameters. The first employs a least squares criterion function and takes into consideration the full structure of the stochastic block model and is evaluated at each point in time. Hence, as an intermediate step, it requires estimating the community structure based on a clustering algorithm at every time point. The second method comprises of the following two steps: in the first one, a least squares function is used and evaluated at each time point, but ignores the community structures and just considers a random graph generating mechanism exhibiting a change point. Once the change point is identified, in the second step, all network data before and after it are used together with a clustering algorithm to obtain the corresponding community structures and subsequently estimate the generating stochastic block model parameters. A comparison between these two methods is illustrated. Further, for both methods under their respective identifiability and certain additional regularity conditions, we establish rates of convergence and derive the asymptotic distributions of the change point estimators. The results are illustrated on synthetic data.