A1271
Title: Bayesian multivariate density-density regression (DDR)
Authors: Peter Mueller - UT Austin (United States) [presenting]
Yang Ni - Texas AM University (United States)
Khai Nguyen - UT Austin (United States)
Abstract: A novel and scalable Bayesian framework for regressing density-valued responses on density-valued predictors is introduced. The motivating application is inference with single-cell gene expression, comparing high-dimensional gene expression under one cell type to that of another cell type. For each patient, the data provides the distribution of gene expression features for both cell types. The proposed approach addresses the critical issue of distributions residing in spaces of differing dimensions. A generalized Bayes framework is utilized, circumventing the need for a fully specified likelihood by employing the sliced Wasserstein distance to measure the discrepancy between fitted and observed distributions. This choice handles high-dimensional data and varying sample sizes efficiently while facilitating a Metropolis-adjusted Langevin algorithm (MALA) for posterior inference. Furthermore, posterior consistency of the generalized Bayesian approach is established, ensuring that the posterior distribution concentrates around the true parameters as the sample size increases. Through simulations and application to a population-scale single-cell dataset, the framework provides robust fits, superior predictive performance compared to traditional methods, and valuable insights into complex biological interactions.
