Robust Mean Estimation

Robust mean estimation focuses on accurately computing the average of a dataset even when a significant portion of the data is corrupted or drawn from a heavy-tailed distribution. Current research emphasizes developing efficient algorithms, often based on filtering techniques or robust variants of Newton's method, that achieve near-optimal error bounds under various contamination models (e.g., Huber contamination, adversarial corruption) and distributional assumptions (e.g., Gaussian, symmetric, sparse). These advancements are crucial for improving the reliability of statistical analyses and machine learning models in the presence of noisy or adversarial data, impacting fields ranging from sensor networks to high-dimensional data analysis.