A0207
Title: Robust inference for high-dimensional logistic regression
Authors: Maria Jaenada - Universidad Complutense Madrid (Spain) [presenting]
Abhik Ghosh - Indian Statistical Institute (India)
Leandro Pardo - Universidad Complutense Madrid (Spain)
Abstract: Real-life data often requires differentiating between two binary classes. In this regard, logistic regression has proven to be a valuable classification technique, offering a straightforward probabilistic interpretation during the classification process. However, in many areas of knowledge, there is a growing need to handle high-dimensional data where the number of variables exceeds the number of observations. High-dimensional data present unique challenges, particularly susceptibility to contamination, which arises from the well-known lack of robustness in classical maximum likelihood methods. To address this issue, a robust procedure is proposed, combining a minimum distance estimator based on the density power divergence (DPD) with regularization techniques, including lasso, adaptive lasso, and non-concave procedures. The proposed techniques find significant applications, especially in scenarios dealing with noisy gene expression data, spectra, and spectral data. Indeed, the practical utility of the techniques is demonstrated in gene selection and patient classification by analyzing real datasets.
