Inferring Hidden Structures in Random Graphs
نویسندگان
چکیده
We study the two inference problems of detecting and recovering an isolated community general structure planted in a random graph. The detection problem is formalized as hypothesis testing problem, where under null hypothesis, graph realization Erdős-Rényi $\mathcal{G(n,q)}$ with edge density notation="LaTeX">$q\in (0,1)$ ; alternative, there unknown notation="LaTeX">$\Gamma _{k}$ on notation="LaTeX">$k$ nodes, , such that it appears xmlns:xlink="http://www.w3.org/1999/xlink">induced subgraph . In case successful detection, we are concerned task corresponding structure. For these problems, investigate fundamental limits from both statistical computational perspectives. Specifically, derive lower bounds for detecting/recovering terms parameters notation="LaTeX">$(n,k,q)$ well certain properties exhibit computationally unbounded optimal algorithms achieve bounds. also consider polynomial-time. As customary many similar structured high-dimensional our model undergoes “easy-hard-impossible” phase transition constraints can severely penalize performance. To provide evidence this phenomenon, show class low-degree polynomials match performance polynomial-time develop.
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ژورنال
عنوان ژورنال: IEEE transactions on signal and information processing over networks
سال: 2022
ISSN: ['2373-776X', '2373-7778']
DOI: https://doi.org/10.1109/tsipn.2022.3211208