On March 23rd, Hieu Cao, a PhD student at Trinity College Dublin, will present a Bayesian approach to regression in the presence of covariate shift. Details for Hieu’s talk are below.
Title
A Bayesian approach for regression in the presence of covariate shift: an application to galaxies redshift estimation.
Abstract
In the regression setting, it is typically assumed that the distributions of covariates in the training and test sets are similar, but this assumption is not always valid. For instance, in sky surveys of galaxies, faint objects are often missed in favour of brighter ones, leading to a covariate shift. Additionally, for data with complex, non-Gaussian distributions, it is crucial to estimate the full conditional density to accurately quantify prediction uncertainty. To address these challenges, we propose a Bayesian approach that employs observation weighting to estimate the conditional density under covariate shift. We consider three different methods for reweighing observations: kernel means matching, optimal transport, and neighbourhood component analysis. Furthermore, we investigate how to incorporate additional features, such as the spatial information of galaxies, into a Gaussian Process model while integrating our reweighting methods. We evaluate our approach using simulated data and demonstrate its effectiveness in mitigating the impact of covariate shift and improving prediction accuracy.