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稠密随机网络中的社群检测AI 解读

We formalize the problem of detecting a community in a network into testing whether in a given (random) graph there is a subgraph that is unusually dense. Specifically, we observe an undirected and unweighted graph on $N$ nodes. Under the null hypothesis, the graph is a realization of an Erdős–Rényi graph with probability $p_{0}$. Under the (composite) alternative, there is an unknown subgraph of $n$ nodes where the probability of connection is $p_{1}>p_{0}$. We derive a…

网络异常簇的检测AI 解读

We consider the problem of detecting whether or not, in a given sensor network, there is a cluster of sensors which exhibit an “unusual behavior.” Formally, suppose we are given a set of nodes and attach a random variable to each node. We observe a realization of this process and want to decide between the following two hypotheses: under the null, the variables are i.i.d. standard normal; under the alternative, there is a cluster of variables that are i.i.d. normal with…

在迷宫中搜寻证据路径AI 解读

Consider a graph with a set of vertices and oriented edges connecting pairs of vertices. Each vertex is associated with a random variable and these are assumed to be independent. In this setting, suppose we wish to solve the following hypothesis testing problem: under the null, the random variables have common distribution N(0, 1) while under the alternative, there is an unknown path along which random variables have distribution N(μ, 1), μ> 0, and distribution N(0, 1) away…