Recovering communities in the general stochastic block model without knowing the parameters
This solves a key limitation in network analysis by enabling parameter-agnostic community detection with theoretical guarantees, though it is incremental in extending known optimality results to more practical settings.
The paper tackles the problem of community detection in the stochastic block model without prior knowledge of model parameters or the number of communities, introducing efficient algorithms that achieve optimal information-theoretic tradeoffs for linear size communities. The results include algorithms for constant, diverging, and logarithmic degree regimes, with quasi-linear complexity and accuracy scaling up to 1-o(1) or optimal limits.
Most recent developments on the stochastic block model (SBM) rely on the knowledge of the model parameters, or at least on the number of communities. This paper introduces efficient algorithms that do not require such knowledge and yet achieve the optimal information-theoretic tradeoffs identified in [AS15] for linear size communities. The results are three-fold: (i) in the constant degree regime, an algorithm is developed that requires only a lower-bound on the relative sizes of the communities and detects communities with an optimal accuracy scaling for large degrees; (ii) in the regime where degrees are scaled by $ω(1)$ (diverging degrees), this is enhanced into a fully agnostic algorithm that only takes the graph in question and simultaneously learns the model parameters (including the number of communities) and detects communities with accuracy $1-o(1)$, with an overall quasi-linear complexity; (iii) in the logarithmic degree regime, an agnostic algorithm is developed that learns the parameters and achieves the optimal CH-limit for exact recovery, in quasi-linear time. These provide the first algorithms affording efficiency, universality and information-theoretic optimality for strong and weak consistency in the general SBM with linear size communities.