Prof. Zhou from Beihang University was invited to give an online academic report at the School of Statistics and Data Science, Nankai University in the afternoon of October 21st, 2022. The topic is "Asymptotics for statistical classification and outlier hypothesis testing". This report was hosted by Yu Lei, Associate professor, School of Statistics and Data Science, Nankai University, and more than 20 teachers and students participated online.
In the presentation, Prof. Zhou first introduced the statistical classification problem in line with real-world machine learning applications, and studied the approximation of its non-asymptotic fundamental limit. In the classical bivariate statistical classification problem, there are training sequences generated from two unknown distributions respectively, and the task is to classify the test sequences that are known to be generated from one of the unknown distributions. Due to finite sample considerations, Prof. Zhou considers a second-order asymptotic trade-off between type I and type II error probabilities to ensure that (1) Type I error probabilities decay exponentially fast for all distribution pairs and (2) type II error probabilities do not disappear for specific distribution pairs. Furthermore, Zhou Lin introduced the second-order approximation results of the non-asymptotic fundamental limit in different scenarios, and discussed the effect of the length ratio between the training sequence and the test sequence on the classification performance, and verified its correctness based on numerical simulation.
Then, Prof. Zhou extended the results of the above binary statistical classification to the outlier hypothesis test problem, and proposed a universality test based on it, and proved that it was second-order asymptotic optimal under the generalized Neyman-Pearson test.
In the lecture, Miss Zhou Lin answered some questions from teachers and students carefully. After the lecture, Prof. Zhou had an in-depth exchange and discussion with the teachers and students on the direction of the follow-up research.
【 Brief Introduction of the Speaker 】
Zhou Lin is an associate researcher and doctoral supervisor at the School of Cyber Science and Technology, Beihang University. His research interests include information theory, physical layer security, wireless communication, statistical anomaly detection, etc. He received his Bachelor's degree in Information Engineering from Shanghai Jiao Tong University in 2014 and his doctorate degree in Electrical and Computer Engineering from the National University of Singapore in 2018. In 2019, it was selected into Beihang University's "100 Outstanding Talents Plan", in 2021, it was selected into the national Young Talent Plan and the 11th batch of Beihang University's "Top Young Talents Plan", and in 2022, it won the first prize of Scientific Progress of the Chinese Command and Control Society.
