报告名称：Matrix-based Rényi’s Entropy: Fast Approximations and Applications

报告专家：龚铁梁

专家所在单位：西安交通大学

报告时间：2023年4月20号 15:30-17：30

报告地点:数统学院203

专家简介：龚铁梁，博士，副教授，硕士生导师。渥太华大学博士后，密歇根大学访问学者。研究方向包括统计学习理论、信息论，机器学习等，并致力于设计具有理论保证的算法应用于临床医学问题。曾获华为2022“揭榜挂帅”项目火花奖，西安交通大学医工交叉青年创新奖。研究成果主要发表于NeurIPS/AAAI, IEEE TSP/TNNLS/TMI/T-CYB/TAC/JBHI, Neural Computation及Nature Scientific Data等国际顶级会议及期刊上。目前担任国际期刊IEEE TIT/TSP/TNNLS/TCYB以及NeurIPS/ICML/AAAI/IJCAI的审稿人，AAAI-2023高级程序委员，作为负责人主持国家自然科学基金青年基金、科技部2030新一代人工智能重大项目子课题，并作为骨干参与国家自然科学基金重点及面上项目多项。

报告摘要：In this talk, we will present computationally efficient approximations to this new entropy functional that can reduce its complexity. Specifically, we leverage the recent progress on Randomized Numerical Linear Algebra, developing Taylor, Chebyshev and Lanczos approximations to tr(G^α), for arbitrary values of α by converting it into a matrix-vector multiplication problem. We also establish the connection between the matrix-based Rényi’s entropy and PSD matrix approximation, which enables exploiting both clustering and block low-rank structure of G to further reduce the computational cost. We theoretically provide approximation accuracy guarantees and illustrate the properties for different approximations. Large-scale experimental evaluations on both synthetic and real-world data corroborate our theoretical findings, showing promising speedup with negligible loss in accuracy.