ROBUST LEARNING UNDER COVARIATE SHIFT AND ANOMALIES

This thesis investigates the role of robustness in machine learning for high-dimensional and safety-critical data, focusing on both covariate shifted regression and anomaly detection. We study robustness to distributional changes in supervised learning, addressing covariate shift in nonparametric regression within reproducing kernel Hilbert spaces (RKHSs). By leveraging random projection techniques, including Nystrom approximations, to restrict the hypothesis space, we achieve substantial computational savings while preserving predictive accuracy under changing input distributions. We also examine robustness in anomaly detection for satellite telemetry. We employ a Controlled Latent Space Model (CLSM), a semi-supervised autoencoder that learns normal operational patterns and enables the detection of anomalies through reconstruction errors. The robustness of the model is evaluated under environmental perturbations and adversarial attacks. The results provide both practical and theoretical insights for monitoring and fault diagnosis, as well as for the development of trustworthy AI systems in operational environments such as satellite telemetry.