Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2011-12-27
Physics
Condensed Matter
Statistical Mechanics
16 pages, 7 figures
Scientific paper
Stochastic blockmodels are generative network models where the vertices are separated into discrete groups, and the probability of an edge existing between two vertices is determined solely by their group membership. In this paper, we derive expressions for the entropy of stochastic blockmodel ensembles. We consider several ensemble variants, including the traditional model as well as the newly introduced degree-corrected version [Karrer et al. Phys. Rev. E {\bf 83}, 016107 (2011)], which imposes a degree sequence on the vertices, in addition to the block structure. The imposed degree sequence is implemented both as "soft" constraints, where only the expected degrees are imposed, and as "hard" constraints, where they are required to be the same on all samples of the ensemble. We also consider generalizations to multigraphs and directed graphs. We illustrate one of many applications of this measure by directly deriving a log-likelihood function from the entropy expression, and using it to infer latent block structure in observed data. Due to the general nature of the ensembles considered, the method works well for ensembles with intrinsic degree correlations (i.e. with entropic origin) as well as extrinsic degree correlations, which go beyond the block structure.
No associations
LandOfFree
The entropy of stochastic blockmodel ensembles does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The entropy of stochastic blockmodel ensembles, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The entropy of stochastic blockmodel ensembles will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-32008