Non Asymptotic

Non-asymptotic analysis in machine learning and statistics focuses on deriving finite-sample guarantees for algorithms and estimators, moving beyond traditional asymptotic analyses that only hold for infinitely large datasets. Current research emphasizes developing non-asymptotic bounds for various models, including recurrent neural networks, transformers, and kernel methods, often employing techniques like concentration inequalities and covering arguments to analyze their performance. This rigorous approach provides more reliable performance guarantees for real-world applications with limited data, improving the trustworthiness and predictability of machine learning models and statistical inference. The resulting theoretical insights are crucial for designing more efficient and robust algorithms across diverse fields.