Abstract

High-dimensional classification studies have become widespread across various domains. The large dimensionality, coupled with the possible presence of data contamination, motivates the use of robust, sparse estimation methods to improve model interpretability and ensure the majority of observations agree with the underlying parametric model. In this study, we propose a robust and sparse estimator for logistic regression models, which simultaneously tackles the presence of outliers and/or irrelevant features. Specifically, we propose the use of $L_0$-constraints and mixed-integer conic programming techniques to solve the underlying double combinatorial problem in a framework that allows one to pursue optimality guarantees. We use our proposal to investigate the main drivers of honey bee (Apis mellifera) loss through the annual winter loss survey data collected by the Pennsylvania State Beekeepers Association. Previous studies mainly focused on predictive performance, however our approach produces a more interpretable classification model and provides evidence for several outlying observations within the survey data. We compare our proposal with existing heuristic methods and non-robust procedures, demonstrating its effectiveness. In addition to the application to honey bee loss, we present a simulation study where our proposal outperforms other methods across most performance measures and settings.

Luca Insolia

Postdoctoral Researcher

My primary research interests concern robust statistics and high-dimensional modeling. During my PhD, I developed statistical methodologies for analyzing sparse regression problems affected by different forms of adversarial data contamination. The developed methodologies encompass continuous optimization methods as well as mixed-integer programming techniques. I applied these tools to analyze biomedical data and to investigate the main possible drivers of honey bee colony loss.

Ana Kenney

Postdoc

Martina Calovi

Associate Professor

Francesca Chiaromonte

Full Professor