Partial Recovery on Random Regular Graphs
نویسندگان
چکیده
The problem of community detection from noisy observations of interactions between individuals has important applications to diverse areas such as biology, sociology, and computer science. This problem is particularly interesting when the number of interactions is on the order of the size of the populations, that is the graph where two interacting individuals are connected by an edge is sparse. One model which has been studied extensively is the labelled stochastic block model. In this model a planted partition is used to generate a random graph with a random edge labelling. In the sparse case the goal is to recover communities which are correlated with the planted partition, that is partially recover the planted partition. Over the course of a number of papers a threshold has been established where partial recovery transitions from impossible to possible. We aim to strengthen these results and find the expected optimal overlap with the planted partition in the regime where partial recovery is possible.
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