Subgaussian Assumption

The subgaussian assumption, a condition specifying that a random variable's tail probabilities decay at least as fast as a Gaussian distribution, is crucial in various machine learning and statistical estimation problems. Current research focuses on extending the applicability of subgaussian-based methods to more complex scenarios, such as Bernoulli reward models in multi-armed bandits, optimal transport problems with non-compactly supported measures, and robust estimation in the presence of outliers. This involves developing new algorithms and theoretical guarantees that relax the stringent requirements of the standard subgaussian assumption, improving the accuracy and efficiency of estimators while maintaining rigorous statistical properties. These advancements have significant implications for diverse fields, including generative modeling, compressed sensing, and differentially private data analysis.