Reliable Time Prediction in the Markov Stochastic Block Model

• URL: http://arxiv.org/abs/2004.04402v2
• Date: Tue, 22 Mar 2022 07:57:23 GMT
• Title: Reliable Time Prediction in the Markov Stochastic Block Model
• Authors: Quentin Duchemin (LAMA)
• Abstract summary: We show how MSBMs can be used to detect dependence structure in growing graphs. We provide methods to solve the so-called link prediction and collaborative filtering problems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce the Markov Stochastic Block Model (MSBM): an extension of the Stochastic Block Model where communities of the nodes are assigned through a Markovian dynamic. We show how MSBMs can be used to detect dependence structure in growing graphs and we provide methods to solve the so-called link prediction and collaborative filtering problems. We make our approaches robust with respect to the outputs of the clustering algorithm and we propose a model selection procedure. Our methods can be applied regardless of the algorithm used to recover communities in the network. In this paper, we use a recent SDP method to infer the hidden communities and we provide theoretical guarantees. In particular, we identify the relevant signal-to-noise ratio (SNR) in our framework and we prove that the misclassification error decays exponentially fast with respect to this SNR.

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