Related papers: Confidence sets in a sparse stochastic block model…
Posterior distributions for community structure in sparse planted bi-section models are shown to achieve exact (resp. almost-exact) recovery, with sharp bounds for the sparsity regimes where edge probabilities decrease as $O(\log(n)/n)$…
We study the frequentist properties of Bayesian statistical inference for the stochastic block model, with an unknown number of classes of varying sizes. We equip the space of vertex labellings with a prior on the number of classes and,…
We show posterior convergence for the community structure in the planted bi-section model, for several interesting priors. Examples include where the label on each vertex is iid Bernoulli distributed, with some parameter $r\in(0,1)$. The…
The stochastic block model is a canonical model of communities in random graphs. It was introduced in the social sciences and statistics as a model of communities, and in theoretical computer science as an average case model for graph…
This paper studies the bounded confidence model on growing fully-mixed populations. In this model, in addition to the usual opinion clusters, significant secondary clusters of smaller size appear systematically, while those secondary…
Clustering is widely studied in statistics and machine learning, with applications in a variety of fields. As opposed to classical algorithms which return a single clustering solution, Bayesian nonparametric models provide a posterior over…
In the sparse normal means model, coverage of adaptive Bayesian posterior credible sets associated to spike and slab prior distributions is considered. The key sparsity hyperparameter is calibrated via marginal maximum likelihood empirical…
With the advent of structured data in the form of social networks, genetic circuits and protein interaction networks, statistical analysis of networks has gained popularity over recent years. Stochastic block model constitutes a classical…
We study community detection in the contextual stochastic block model arXiv:1807.09596 [cs.SI], arXiv:1607.02675 [stat.ME]. In arXiv:1807.09596 [cs.SI], the second author studied this problem in the setting of sparse graphs with…
Mixture model-based frameworks are very popular for statistical inference in clustering. While convenient for producing probabilistic estimates of cluster assignments and uncertainty, they are prone to misspecification, which can lead to…
The proposed approach extends the confidence posterior distribution to the semi-parametric empirical Bayes setting. Whereas the Bayesian posterior is defined in terms of a prior distribution conditional on the observed data, the confidence…
By representing the range of fair betting odds according to a pair of confidence set estimators, dual probability measures on parameter space called frequentist posteriors secure the coherence of subjective inference without any prior…
Bayesian clustering methods have the widely touted advantage of providing a probabilistic characterization of uncertainty in clustering through the posterior distribution. An amazing variety of priors and likelihoods have been proposed for…
We propose a Machine Learning approach for optimal macroeconomic density forecasting in a high-dimensional setting where the underlying model exhibits a known group structure. Our approach is general enough to encompass specific forecasting…
In this paper, we study the information-theoretic limits of community detection in the symmetric two-community stochastic block model, with intra-community and inter-community edge probabilities $\frac{a}{n}$ and $\frac{b}{n}$ respectively.…
For estimating a lower bounded parametric function in the framework of Marchand and Strawderman (2006), we provide through a unified approach a class of Bayesian confidence intervals with credibility $1-\alpha$ and frequentist coverage…
Stochastic Block Models (SBMs) are a fundamental tool for community detection in network analysis. But little theoretical work exists on the statistical performance of Bayesian SBMs, especially when the community count is unknown. This…
We consider community detection from multiple correlated graphs sharing the same community structure. The correlated graphs are generated by independent subsampling of a parent graph sampled from the stochastic block model. The vertex…
Modern regression applications can involve hundreds or thousands of variables which motivates the use of variable selection methods. Bayesian variable selection defines a posterior distribution on the possible subsets of the variables…
Bayesian methods provide a natural means for uncertainty quantification, that is, credible sets can be easily obtained from the posterior distribution. But is this uncertainty quantification valid in the sense that the posterior credible…