Consensus Monte Carlo for Random Subsets using Shared Anchors
arXiv:1906.12309
Abstract
We present a consensus Monte Carlo algorithm that scales existing Bayesian nonparametric models for clustering and feature allocation to big data. The algorithm is valid for any prior on random subsets such as partitions and latent feature allocation, under essentially any sampling model. Motivated by three case studies, we focus on clustering induced by a Dirichlet process mixture sampling model, inference under an Indian buffet process prior with a binomial sampling model, and with a categorical sampling model. We assess the proposed algorithm with simulation studies and show results for inference with three datasets: an MNIST image dataset, a dataset of pancreatic cancer mutations, and a large set of electronic health records (EHR). Supplementary materials for this article are available online.
References in corpus (13)
- Discussion on Bayesian Cluster Analysis: Point Estimation and Credible Balls by Sara Wade and Zoubin Ghahramani
- Bayesian cluster analysis: Point estimation and credible balls
- Are Gibbs-type priors the most natural generalization of the Dirichlet process?
- MCMC for Normalized Random Measure Mixture Models
- Coresets for Scalable Bayesian Logistic Regression
- Parallelizing MCMC via Weierstrass Sampler
- Automated Scalable Bayesian Inference via Hilbert Coresets
- MAD-Bayes: MAP-based Asymptotic Derivations from Bayes
- Cluster and Feature Modeling from Combinatorial Stochastic Processes
- MAD Bayes for Tumor Heterogeneity Feature Allocation with Non-Normal Sampling
- A Bayesian feature allocation model for tumor heterogeneity
- Scaling the Indian Buffet Process via Submodular Maximization
- Variational consensus Monte Carlo