The Degree-Corrected Stochastic Block Model (DCSBM) is a popular model to generate random graphs with community structure given an expected degree sequence. The standard approach of community detection based on the DCSBM is to search for the model parameters that are the most likely to have produced the observed network data through maximum likelihood estimation (MLE). Current techniques for the MLE problem are heuristics, and therefore do not guarantee convergence to the optimum. We present mathematical programming formulations and exact solution methods that can provably find the model parameters and community assignments of maximum likelihood given an observed graph. We compare these exact methods with classical heuristic algorithms based on expectation-maximization (EM). The solutions given by exact methods give us a principled way of measuring the experimental performance of classical heuristics and comparing different variations thereof.
翻译:学位校正的斯托切斯特区块模型(DCSBM)是一个广受欢迎的模型,可以生成随机图解,以社区结构为预期的分级序列。基于DCSBM的社区探测标准方法是寻找最有可能通过最大可能性估计(MLE)生成所观测网络数据的模型参数。目前MLE问题的当前技术是超自然学,因此不能保证与最佳一致。我们提出了数学编程配方和精确的解决方案,可以找到模型参数和所观测的图表所显示的最大可能性社区分配。我们将这些精确的方法与基于预期最大化的经典超常算法(EM)进行比较。精确方法给出的解决方案为我们提供了测量古典超自然学实验性能和比较不同变化的有原则的方法。