Honey bee (Apis mellifera) colony loss is a widespread phenomenon with important economic and biological implications, whose drivers are still an open matter of investigation. We contribute to this line of research through a large-scale, multi-variable study combining multiple publicly accessible data sources. Specifically, we analyzed quarterly data covering the contiguous United States for the years 2015-2021, and combined open data on honey bee colony status and stressors, weather data, and land use. The different spatio-temporal resolutions of these data are addressed through an up-scaling approach that generates additional statistical features which capture more complex distributional characteristics and significantly improve modeling performance. Treating this expanded feature set with state-of-the-art feature selection methods, we obtained findings that, nation-wide, are in line with the current knowledge on the aggravating roles of Varroa destructor and pesticides in colony loss. Moreover, we found that extreme temperature and precipitation events, even when controlling for other factors, significantly impact colony loss. Overall, our results reveal the complexity of biotic and abiotic factors affecting managed honey bee colonies across the United States.

Biomedical research is increasingly data rich, with studies comprising ever growing numbers of features. The larger a study, the higher the likelihood that a substantial portion of the features may be redundant and/or contain contamination (outlying values). This poses serious challenges, which are exacerbated in cases where the sample sizes are relatively small. Effective and efficient approaches to perform sparse estimation in the presence of outliers are critical for these studies, and have received considerable attention in the last decade. We contribute to this area considering high‐dimensional regressions contaminated by multiple mean‐shift outliers affecting both the response and the design matrix. We develop a general framework and use mixed‐integer programming to simultaneously perform feature selection and outlier detection with provably optimal guarantees. We prove theoretical properties for our approach, that is, a necessary and sufficient condition for the robustly strong oracle property, where the number of features can increase exponentially with the sample size; the optimal estimation of parameters; and the breakdown point of the resulting estimates. Moreover, we provide computationally efficient procedures to tune integer constraints and warm‐start the algorithm. We show the superior performance of our proposal compared to existing heuristic methods through simulations and use it to study the relationships between childhood obesity and the human microbiome.

Sparse estimation methods capable of tolerating outliers have been broadly investigated in the last decade. We contribute to this research considering high-dimensional regression problems contaminated by multiple mean-shift outliers which affect both the response and the design matrix. We develop a general framework for this class of problems and propose the use of mixed-integer programming to simultaneously perform feature selection and outlier detection with provably optimal guarantees. We characterize the theoretical properties of our approach, i.e. a necessary and sufficient condition for the robustly strong oracle property, which allows the number of features to exponentially increase with the sample size; the optimal estimation of the parameters; and the breakdown point of the resulting estimates. Moreover, we provide computationally efficient procedures to tune integer constraints and to warm-start the algorithm. We show the superior performance of our proposal compared to existing heuristic methods through numerical simulations and an application investigating the relationships between the human microbiome and childhood obesity.