Central Limit Theorem

The Central Limit Theorem (CLT) describes the tendency of the average of many independent random variables to approximate a normal distribution, regardless of the original variables' distributions. Current research focuses on extending CLT's applicability to more complex scenarios, including dependent data (e.g., Markov chains, time series), and analyzing its implications within specific algorithms like stochastic gradient descent and Bayesian neural networks, as well as in applications such as queuing theory and bandit algorithms. These advancements provide rigorous statistical guarantees for a wide range of machine learning and statistical methods, improving the reliability of inference and estimation in diverse fields.