Explore a comprehensive lecture on simultaneous feature selection and outlier detection using mixed-integer programming with optimality guarantees. Delve into the challenges of biomedical research with increasing data complexity and learn about a novel approach to handle high-dimensional regressions contaminated by multiple mean-shift outliers. Discover the general framework developed using mixed-integer programming, its theoretical properties, and computationally efficient procedures for tuning and warm-starting the algorithm. Compare the performance of this proposal to existing heuristic methods through simulations and examine its application in studying relationships between early infant weight gain and the human microbiome. Gain insights from Ana Kenney, a postdoctoral researcher at UC Berkeley, as she presents her work at the intersection of computational statistics, machine learning, and optimization applied to biomedical sciences.