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.

中文翻译：

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逐步的Tikhonov正则化：在HIV-1耐药性预测中的应用。

本文着重于构建HIV抗逆转录病毒药物敏感性的基因型预测因子。为此，开发了一种在最小二乘问题中恢复未知矢量的最大元素的方法。所提出的方法引入了两个新颖的思想。第一个想法是基于候选变量的估计量的新颖的向前逐步选择过程。为了实现此新引入的过程，我们从稀疏表示的角度修订了Tikhonov正则化。通过这种分析，我们得出了本文中的第二个新想法，这是开发一种在最小二乘问题中恢复未知向量最大元素的新方法。该方法实现了一系列Tikhonov正则化问题，旨在恢复未知矢量的剩余元素中的最大元素。此外，我们得出足够的条件来确保回收未知向量的最大元素。我们使用模拟数据和来自Stanford HIV抗性数据库的数据进行数值研究。将所提出的方法的性能与最新方法进行了比较。