Sparse Popularity Adjusted Stochastic Block Model
In the present paper we study a sparse stochastic network enabled with a block structure. The popular Stochastic Block Model (SBM) and the Degree Corrected Block Model (DCBM) address sparsity by placing an upper bound on the maximum probability of connections between any pair of nodes. As a result, sparsity describes only the behavior of network as a whole, without distinguishing between the block-dependent sparsity patterns. To the best of our knowledge, the recently introduced Popularity Adjusted Block Model (PABM) is the only block model that allows to introduce a {\it structural sparsity} where some probabilities of connections are identically equal to zero while the rest of them remain above a certain threshold. The latter presents a more nuanced view of the network.
Code (0)
등록된 구현이 없습니다.
Tasks
modelStochastic Block ModelSimilar Papers 제목 키워드 기반
Popularity Adjusted Block Models are Generalized Random Dot Product Graphs
We connect two random graph models, the Popularity Adjusted Block Model (PABM) and the Generalized Random Dot Product Graph (GRDPG), by demonstrating that the PABM is a special case of the GRDPG in which communities corr…
ClusteringCommunity Detectionparameter estimationThe Hierarchy of Block Models
There exist various types of network block models such as the Stochastic Block Model (SBM), the Degree Corrected Block Model (DCBM), and the Popularity Adjusted Block Model (PABM). While this leads to a variety of choice…
ClusteringStochastic Block ModelHypothesis Testing for Equality of Latent Positions in Random Graphs
We consider the hypothesis testing problem that two vertices $i$ and $j$ of a generalized random dot product graph have the same latent positions, possibly up to scaling. Special cases of this hypothesis test include tes…
Model SelectionStochastic Block ModelOptimal Graph Clustering without Edge Density Signals
This paper establishes the theoretical limits of graph clustering under the Popularity-Adjusted Block Model (PABM), addressing limitations of existing models. In contrast to the Stochastic Block Model (SBM), which assume…
Graph ClusteringStrongly Consistent Community Detection in Popularity Adjusted Block Models
The Popularity Adjusted Block Model (PABM) provides a flexible framework for community detection in network data by allowing heterogeneous node popularity across communities. However, this flexibility increases model com…
ClusteringCommunity Detection