Statistics and Computational Methods Seminar Series - 2024/25

Speaker: David Dunson and Amy Herring (Duke University)

Title: Collaborations motivating theory: extensions of latent class regression

Abstract

Numerous successful senior researchers note their methods research is driven by their collaborations - while the "why" may be obvious, the "how" is often a mystery. Using examples from health research and ecology, we describe “original” analysis goals and plans, unforeseen challenges, resulting methodological innovations, and opportunities still being explored in a biomedical study, before going in depth with an example in deep latent class regression, where high-dimensional categorical data arise in diverse scientific domains and are often accompanied by covariates. Latent class regression models are routinely used in such settings, reducing dimensionality by assuming conditional independence of the categorical variables given a single latent class that depends on covariates through a logistic regression model. However, such methods become unreliable as the dimensionality increases. To address this, we propose a flexible family of deep latent class models. Our model satisfies key theoretical properties, including identifiability and posterior consistency, and we establish a Bayes oracle clustering property that ensures robustness against the curse of dimensionality. We develop efficient posterior computation methods, validate them through simulation studies, and apply our model to joint species distribution modeling in ecology. The theory and methods can be easily extended beyond categorical observed data.

Link Google Meet: meet.google.com/ctv-bcfy-fof