论文标题
随机步行访问的密集随机块模型的估计
Estimation of dense stochastic block models visited by random walks
论文作者
论文摘要
我们有兴趣从探索随机步行发现的子图中恢复随机块模型上的信息。随机块模型对应于构成有限数量类型的种群，其中两个个体由边缘与另一对独立于边缘连接，并取决于它们的类型。在这里，我们考虑使用图形可以近似随机网络的密集情况。该问题是由于对链条转诊调查的研究引发的，在该研究中，每个受访者在社交网络中提供有关其联系的信息。首先，我们写出随机步行发现的子图的可能性：出现偏见，因为轮毂和大多数类型更有可能被采样。即使在观察到类型的情况下，最大似然估计器也不再明确。当未观察到顶点的类型时，我们使用SAEM算法来最大化可能性。其次，我们使用Athreya和Roellin的新结果提出了不同的估计策略。它包括消除Daudin等人提出的最大似然估计量。这忽略了偏见。
We are interested in recovering information on a stochastic block model from the subgraph discovered by an exploring random walk. Stochastic block models correspond to populations structured into a finite number of types, where two individuals are connected by an edge independently from the other pairs and with a probability depending on their types. We consider here the dense case where the random network can be approximated by a graphon. This problem is motivated from the study of chain-referral surveys where each interviewee provides information on her/his contacts in the social network. First, we write the likelihood of the subgraph discovered by the random walk: biases are appearing since hubs and majority types are more likely to be sampled. Even for the case where the types are observed, the maximum likelihood estimator is not explicit any more. When the types of the vertices is unobserved, we use an SAEM algorithm to maximize the likelihood. Second, we propose a different estimation strategy using new results by Athreya and Roellin. It consists in de-biasing the maximum likelihood estimator proposed in Daudin et al. and that ignores the biases.
