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多层随机点积图：估计与在线变点检测AI 解读

Abstract We study the multilayer random dot product graph (MRDPG) model, a generalization of the random dot product graph model to multilayer networks. To estimate the edge probabilities, we deploy a tensor-based methodology and demonstrate its superiority over existing approaches. Moving to dynamic MRDPGs, we formulate and analyse an online change point detection framework, where, at each time point, we observe a realization from an MRDPG. Across layers, we assume fixed…

范旺、余怡与里纳尔多对网络潜在生长过程根与社区推断的讨论AI 解读

We congratulate Prof. Crane and Dr Xu for introducing a very interesting and appealing statistical model for Markovian network growth. The PAPER model enjoys several qualities. In particular, (i) it strikes a rare balance between analytic elegance and tractability, and expressive power; (ii) it allows for practicable algorithms for statistical inference that scale to networks of very large size, and (iii) it is very flexible and can be readily generalized to model a variety…

稀疏动态网络中变点的最优检测与定位AI 解读

We study the problem of change point localization in dynamic networks models. We assume that we observe a sequence of independent adjacency matrices of the same size, each corresponding to a realization of an unknown inhomogeneous Bernoulli model. The underlying distribution of the adjacency matrices are piecewise constant, and may change over a subset of the time points, called change points. We are concerned with recovering the unknown number and positions of the change…

随机网络、图模型与可交换性AI 解读

Summary We study conditional independence relationships for random networks and their interplay with exchangeability. We show that, for finitely exchangeable network models, the empirical subgraph densities are maximum likelihood estimates of their theoretical counterparts. We then characterize all possible Markov structures for finitely exchangeable random graphs, thereby identifying a new class of Markov network models corresponding to bidirected Kneser graphs. In…

β 模型中的最大似然估计AI 解读

We study maximum likelihood estimation for the statistical model for undirected random graphs, known as the $\beta$-model, in which the degree sequences are minimal sufficient statistics. We derive necessary and sufficient conditions, based on the polytope of degree sequences, for the existence of the maximum likelihood estimator (MLE) of the model parameters. We characterize in a combinatorial fashion sample points leading to a nonexistent MLE, and nonestimability of the…

指数随机图模型的抽样一致性AI 解读

The growing availability of network data and of scientific interest in distributed systems has led to the rapid development of statistical models of network structure. Typically, however, these are models for the entire network, while the data consists only of a sampled sub-network. Parameters for the whole network, which is what is of interest, are estimated by applying the model to the sub-network. This assumes that the model is consistent under sampling, or, in terms of…