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DYNAMIC NETWORK MODELS AND GRAPHON ESTIMATION
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DOI：10.1214/18-AOS1751.png)
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摘要
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In the present paper, we consider a dynamic stochastic network model. The objective is estimation of the tensor of connection probabilities Lambda when it is generated by a Dynamic Stochastic Block Model (DSBM) or a dynamic graphon. In particular, in the context of the DSBM, we derive a penalized least squares estimator (Lambda) over cap of Lambda and show that (Lambda) over cap satisfies an oracle inequality and also attains minimax lower bounds for the risk. We extend those results to estimation of Lambda when it is generated by a dynamic graphon function. The estimators constructed in the paper are adaptive to the unknown number of blocks in the context of the DSBM or to the smoothness of the graphon function. The technique relies on the vectorization of the model and leads to much simpler mathematical arguments than the ones used previously in the stationary set up. In addition, all results in the paper are nonasymptotic and allow a variety of extensions.
Keyword:
Dynamic network
graphon
stochastic block model
nonparametric regression
minimax rate
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