TY - JOUR

T1 - Parsimonious module inference in large networks

AU - Peixoto, Tiago P.

PY - 2013/4/5

Y1 - 2013/4/5

N2 - We investigate the detectability of modules in large networks when the number of modules is not known in advance. We employ the minimum description length principle which seeks to minimize the total amount of information required to describe the network, and avoid overfitting. According to this criterion, we obtain general bounds on the detectability of any prescribed block structure, given the number of nodes and edges in the sampled network. We also obtain that the maximum number of detectable blocks scales as √N, where N is the number of nodes in the network, for a fixed average degree ⟨k⟩. We also show that the simplicity of the minimum description length approach yields an efficient multilevel Monte Carlo inference algorithm with a complexity of O(τNlogN), if the number of blocks is unknown, and O(τN) if it is known, where τ is the mixing time of the Markov chain. We illustrate the application of the method on a large network of actors and films with over 106 edges, and a dissortative, bipartite block structure.

AB - We investigate the detectability of modules in large networks when the number of modules is not known in advance. We employ the minimum description length principle which seeks to minimize the total amount of information required to describe the network, and avoid overfitting. According to this criterion, we obtain general bounds on the detectability of any prescribed block structure, given the number of nodes and edges in the sampled network. We also obtain that the maximum number of detectable blocks scales as √N, where N is the number of nodes in the network, for a fixed average degree ⟨k⟩. We also show that the simplicity of the minimum description length approach yields an efficient multilevel Monte Carlo inference algorithm with a complexity of O(τNlogN), if the number of blocks is unknown, and O(τN) if it is known, where τ is the mixing time of the Markov chain. We illustrate the application of the method on a large network of actors and films with over 106 edges, and a dissortative, bipartite block structure.

UR - http://dx.doi.org/10.1103/PhysRevLett.110.148701

U2 - 10.1103/PhysRevLett.110.148701

DO - 10.1103/PhysRevLett.110.148701

M3 - Article

SN - 0031-9007

VL - 110

JO - Physical Review Letters

JF - Physical Review Letters

M1 - 169905

ER -