Large Deviation
Large deviation theory analyzes the probabilities of rare events—outcomes significantly deviating from expected behavior—in various systems. Current research focuses on extending its application to high-dimensional data, particularly in machine learning contexts, using techniques like stochastic gradient descent analysis and refined asymptotic approximations to improve accuracy in estimating error probabilities. This work is crucial for enhancing the reliability and efficiency of algorithms in diverse fields, including machine learning model training, distributed inference, and the analysis of stochastic dynamical systems. Improved understanding of large deviations offers more precise performance guarantees and enables the design of more robust and efficient algorithms.