Moderator: Gwen Jacobson
Speakers: Alexander Dombowsky and Yuren Zhou
Speaker: Alex Dombowsky
Title: Bayesian Clustering via Fusing of Localized Densities
Abstract: Bayesian clustering typically relies on mixture models, with each component interpreted as a different cluster. After defining a prior for the component parameters and weights, Markov chain Monte Carlo (MCMC) algorithms are commonly used to produce samples from the posterior distribution of the component labels. The data are then clustered by minimizing the expectation of a clustering loss function that favors similarity to the component labels. Unfortunately, although these approaches are routinely implemented, clustering results are highly sensitive to kernel misspecification. For example, if Gaussian kernels are used but the true density of data within a cluster is even slightly non-Gaussian, then clusters will be broken into multiple Gaussian components. To address this problem, we develop Fusing of Localized Densities (FOLD), a novel clustering method that melds components together using the posterior of the kernels. FOLD has a fully Bayesian decision theoretic justification, naturally leads to uncertainty quantification, can be easily implemented as an add-on to MCMC algorithms for mixtures, and favors a small number of distinct clusters. We provide theoretical support for FOLD including clustering optimality under kernel misspecification. In simulated experiments and real data, FOLD outperforms competitors by minimizing the number of clusters while inferring meaningful group structure.
Preprint: https://arxiv.org/abs/2304.00074
Speaker: Yuren Zhou
Title: Bayesian Pyramids with Covariates with Application in Ecology
Abstract: Joint Species Distribution Modeling (JSDM) aims to model the joint distribution of multiple species occurrences and their dependencies on environmental predictors. Traditional JSDM approaches often rely on continuous latent variables to capture dependencies between species occurrences. In this work, we propose a novel approach using multidimensional discrete latent variables, extending the Bayesian Pyramids method to incorporate both sample and meta covariates. Our method demonstrates desirable theoretical properties, including strict and generic identifiability, posterior consistency, and a Bayesian oracle property for deep latent cluster that escapes the curse of dimensionality. We analyze asymptotic regimes where both sample size N and number of species p go to infinity. Preliminary simulation results and application to a Finnish bird dataset are provided. This is an ongoing work with Yuqi Gu and David Dunson, currently in its early stages.