A variational Bayes approach to debiased inference in high-dimensional linear regression

Kolyan Ray (Imperial College London)

Wednesday 11th June 14:00-15:00
Maths 311B

Abstract

We consider statistical inference for a single coordinate of a high-dimensional parameter in sparse linear regression. It is well-known that high-dimensional procedures such as the LASSO can provide biased estimators for this problem and thus require debiasing. We propose a scalable variational Bayes method for this problem based on assigning a mean-field approximation to the nuisance coordinates and carefully modelling the conditional distribution of the target given the nuisance. We investigate the numerical performance of our algorithm and establish accompanying theoretical guarantees for estimation and uncertainty quantification.

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