Unfolding Generalized Shannon’s Entropy
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：张镓麟（美国Mississippi State University）
：2025-12-24 15:00
：海韵园实验楼S204
报告人：张镓麟（美国Mississippi State University）
时 间：2025年12月24日15:00
地 点：海韵园实验楼S204
内容摘要:
Shannon’s entropy is a cornerstone of information theory, quantifying uncertainty within a probability distribution. However, the classical definition may fail for distributions with heavy tails on infinite alphabets, leaving gaps in its theoretical foundation. This talk introduces a framework called Generalized Shannon’s Entropy (GSE), which extends the original concept to ensure well-definedness and robustness under broader conditions.
The talk begins by revisiting Shannon’s entropy and its limitations, followed by the construction of the GSE through escort distributions that adjust tail behavior. The asymptotic properties of plug-in estimators for GSE are discussed, including a central limit theorem that requires minimal assumptions. The talk then connects this generalization to mutual information, leading to tests of independence on a contingency table with asymptotic normality.
The second half explores the role of GSE in characterizing discrete probability distributions. Several recent results are reviewed, showing how finite or countable infinite sets of entropic quantities can uniquely determine a distribution up to permutation. The talk concludes with open directions toward developing goodness-of-fit tests for discrete and disparate sample spaces using finite-order GSE characterization.
个人简介：
Dr. Jialin Zhang is an Assistant Professor of Statistics at Mississippi State University. He received bachelor degree in Mathematics and Applied Mathematics from Xiamen University in 2012 and his Ph.D. in Statistics from the University of North Carolina at Charlotte in 2019 before joining Mississippi State University. His research focuses on nonparametric estimation of information-theoretic quantities and entropic approaches to statistical inference. His works have appeared on Statistics and Probability Letters, Entropy, Machine Learning and Knowledge Extraction, Communications in Statistics-Theory and Methods.
联系人：谭志裕
