Stepwise Tikhonov Regularisation: Application to the Prediction of HIV-1 Drug Resistance

This paper focuses on constructing genotypic predictors for antiretroviral drug susceptibility of HIV. To this end, a method to recover the largest elements of an unknown vector in a least squares problem is developed. The proposed method introduces two novel ideas. The first idea is a novel forward stepwise selection procedure based on the magnitude of the estimates of the candidate variables. To implement this newly introduced procedure, we revise Tikhonov regularisation from a sparse representations' perspective. This analysis leads us to the second novel idea in the paper, which is the development of a new method to recover the largest elements of the unknown vector in the least squares problem. The method implements a sequence of Tikhonov regularisation problems which aim to recover the largest of the remaining elements of the unknown vector. Additionally, we derive sufficient conditions that ensure the recovery of the largest elements of the unknown vector. We perform numerical studies using simulated data and data from the Stanford HIV resistance database. The performance of the proposed method is compared against a state-of-the-art method.