\dm_csml_event_details UCL ELLIS

Inference in high-dimensional logistic regression models with separated data


Rebecca Lewis


Imperial College London


Friday, 24 June 2022




Function Space, UCL Centre for Artificial Intelligence, 1st Floor, 90 High Holborn, London WC1V 6BH



Event series

DeepMind/ELLIS CSML Seminar Series


Existence of the maximum likelihood estimate of logistic regression coefficients requires that the observed sequence of covariate and response values are not linearly separable. Even when the maximum likelihood estimator exists, it can suffer from considerable bias when the number of independent observations is not large relative to the dimension. We propose an alternative approach to inference on the logistic regression coefficients based on a corrected ordinary least squares estimator. Consistency and asymptotic normality of this estimator is established under a high-dimensional regime in which the number p of covariates and the sample size n both tend to infinity with p < n under weak conditions on the design matrix. Validity of Wald-based inference through this route is thereby established, even when maximum likelihood is infeasible.


Rebecca is a third-year PhD student working in the area of high-dimensional statistics under the supervision of Dr Heather Battey. Her research focuses on the construction of a confidence set of models, a set that includes a small number of models that fit the data essentially equally well, and other topics derived from this, including the one given in this talk.