A Tractable Fully Bayesian Method for the Stochastic Block Model
The stochastic block model (SBM) is a generative model revealing macroscopic structures in graphs. Bayesian methods are used for (i) cluster assignment inference and (ii) model selection for the number of clusters. In this paper, we study the behavior of Bayesian inference in the SBM in the large sample limit. Combining variational approximation and Laplace's method, a consistent criterion of the fully marginalized log-likelihood is established. Based on that, we derive a tractable algorithm that solves tasks (i) and (ii) concurrently, obviating the need for an outer loop to check all model candidates. Our empirical and theoretical results demonstrate that our method is scalable in computation, accurate in approximation, and concise in model selection.
Code (0)
등록된 구현이 없습니다.
Tasks
Bayesian InferenceModel SelectionStochastic Block ModelSimilar Papers 제목 키워드 기반
Variational Inference for Latent Variable Models in High Dimensions
Variational inference (VI) is a popular method for approximating intractable posterior distributions in Bayesian inference and probabilistic machine learning. In this paper, we introduce a general framework for quantifyi…
Bayesian InferenceVariational InferenceVector Copula Variational Inference and Dependent Block Posterior Approximations
Variational inference (VI) is a popular method to estimate statistical and econometric models. The key to VI is the selection of a tractable density to approximate the Bayesian posterior. For large and complex models a c…
Variational InferenceBayesian Model Selection of Stochastic Block Models
A central problem in analyzing networks is partitioning them into modules or communities. One of the best tools for this is the stochastic block model, which clusters vertices into blocks with statistically homogeneous p…
modelModel SelectionStochastic Block ModelAdvances in Variational Inference
Many modern unsupervised or semi-supervised machine learning algorithms rely on Bayesian probabilistic models. These models are usually intractable and thus require approximate inference. Variational inference (VI) lets …
Variational InferencePrivacy for Free: Posterior Sampling and Stochastic Gradient Monte Carlo
We consider the problem of Bayesian learning on sensitive datasets and present two simple but somewhat surprising results that connect Bayesian learning to "differential privacy:, a cryptographic approach to protect indi…