Information Theory, Probability and Statistical Learning

In 2024, Andrew Barron turned 65 and retired. This is a Festschrift volume honoring his career and contributions. Andrew R. Barron, a professor of Statistics and Data Science at Yale University, has been one of the most influential figures in information theory research over the past 40 years. He has made profound, broad and consistent contributions to information theory, as well as its interactions with probability theory, statistical learning, and neural networks. From his Ph.D. thesis work in 1985 until today, Barron has been recognized as a leader in both information theory and statistics, especially in the area where the two fields intersect and fertilize each other. There has been a powerful tradition of important work on this interface and it has had a strong impact on both fields. Through the introduction of novel ideas and techniques, and through his outstanding scholarship, Barron has clarified some of the foundations of the mathematical and statistical side of Shannon theory, and he has helped solidify our understanding of the connection between information theory and statistics. This volume consists of invited papers, by prominent researchers that either personally or through the topics of the work have some connection with Barron. The papers in this volume are written by people working in all three areas where Barron has made major contributions: Information theory, probability, and statistical learning. These topics are very timely as there is major current activity in all three areas, especially in connection with the explosive current advances in machine learning theory and its applications.