A0822
Title: Bayesian methods for regression with confounding variables
Authors: Luke Travis - Imperial College London (United Kingdom) [presenting]
Abstract: Bayesian methods are developed for regression models in the presence of unobserved confounding variables. Confounded versions of both the sparse high-dimensional linear regression and nonparametric regression settings are considered. Under suitable conditions on the prior, the Bayesian posterior contracts to the truth at the same rate, with no confounding, and which has the same order as the L1-loss provided by frequentist methods. Moreover, it is illustrated that for a specific choice of prior covariance, the spectral obtained transforms the proposed by a frequentist counterpart. The strong performance of the Bayesian method (and a computationally scalable variational approximation) is demonstrated in terms of estimation and model selection in a variety of different scenarios. Moreover, it is shown that the out-of-the-box uncertainty quantification provided by the posterior is reliable.
