Title: Efficient Estimators for Heavy-Tailed Machine Learning. Abstract: A dramatic improvement in data collection technologies has aided in procuring massive amounts of unstructured and heterogeneous datasets. This has consequently led to a prevalence of heavy-tailed distributions across a broad range of tasks in machine learning. In this work, we perform thorough empirical studies to show that modern machine learning models such as generative adversarial networks and invertible flow models are plagued with such ill-behaved distributions during the phase of training them. To alleviate this problem, we develop a computationally-efficient estimator for mean estimation with provable guarantees which can handle such ill-behaved distributions. We provide specific consequences of our theory for supervised learning tasks such as linear regression and generalized linear models. Furthermore, we study the performance of our algorithm on synthetic tasks and real-world experiments and show that our methods convincingly outperform a variety of practical baselines.