Reliable prediction in the Markov stochastic block model

LAMA, Univ Gustave Eiffel, Univ Paris Est Créteil, CNRS, 77447 Marne-la-Vallée, France

^* Corresponding author: quentin.duchemin@univ-eiffel.fr

Received: 3 June 2022
Accepted: 28 November 2022

Abstract

We introduce the Markov Stochastic Block Model (MSBM): a growth model for community based networks where node attributes are assigned through a Markovian dynamic. We rely on HMMs’ literature to design prediction methods that are robust to local clustering errors. We focus specifically on the link prediction and collaborative filtering problems and we introduce a new model selection procedure to infer the number of hidden clusters in the network. Our approaches for reliable prediction in MSBMs are not algorithm-dependent in the sense that they can be applied using your favourite clustering tool. 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.