  Penalized logistic regression is extremely useful for binary classification
with large number of covariates (higher than the sample size), having several
real life applications, including genomic disease classification. However, the
existing methods based on the likelihood loss function are sensitive to data
contamination and other noise and, hence, robust methods are needed for stable
and more accurate inference. In this paper, we propose a family of robust
estimators for sparse logistic models utilizing the popular density power
divergence based loss function and the general adaptively weighted LASSO
penalties. We study the local robustness of the proposed estimators through its
influence function and also derive its oracle properties and asymptotic
distribution. With extensive empirical illustrations, we demonstrate the
significantly improved performance of our proposed estimators over the existing
ones with particular gain in robustness. Our proposal is finally applied to
analyse four different real datasets for cancer classification, obtaining
robust and accurate models, that simultaneously performs gene selection and
patient classification.
