Optimal Recovery

Optimal recovery focuses on reconstructing complete data from incomplete or noisy observations, a crucial problem across diverse fields. Current research emphasizes efficient algorithms for recovering data from various sources, including compressed measurements, poisoned datasets in federated learning, and partially observed graph signals, often employing techniques like matrix completion, regularized optimization, and message-passing algorithms. These advancements improve the accuracy and efficiency of data recovery in applications ranging from machine learning and signal processing to genomic sequencing and grid resilience analysis, ultimately leading to more robust and reliable data-driven systems. The development of provably optimal or near-optimal recovery methods, particularly concerning hyperparameter selection, is a key area of ongoing investigation.