Bayesian Deep Latent Class Regression

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.