Leo Duan is currently an assistant professor at University of Florida. His research interest focuses on statistical modeling for combinatorial problems, leveraging the new tools his lab develops at the interface between Bayesian methodology and optimization. His research works are largely driven by data science applications, in particular those for improving the understanding of the human brain, and strengthening the robustness of America's infrastructure.
Talk: Graphical Model-based Clustering: A New Hope
Abstact: Model-based clustering is a compelling framework for characterizing data heterogeneity and supporting Bayesian nonparametric data analysis. Typically, we specify a mixture likelihood consisting of mixture weights and components, where data points assigned to the same cluster are treated as conditionally i.i.d. from a component distribution. Although a rich literature has been developed, correctly specifying the component distribution remains a significant challenge, and a lack of robustness in clustering is both widely observed and theoretically established.
In this talk, I will present a new model-based clustering approach leveraging graphical models. In this framework, data points are assumed to arise dependently according to an unknown disjoint union of component graphs. Taking a Bayesian approach, I can marginalize out the edges as non-meaningful latent variables, and estimate the integrated posterior on the node partition, equivalent to the clustering of the data points. I will primarily focus on models using spanning forest graphs and highlight several theoretical advancements, including tractable marginal posterior, proximity between the posterior mode and a spectral clustering estimator, and robust consistency under model misspecification. I will illustrate the practical utility in a neuroscience application of clustering multi-subject functional Magnetic Resonance Imaging data from an Alzheimer’s disease study.