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DATA8015 - Mathematical Foundation of Data Science

Foundation

Course Instructor

Professor Yingyu LIANG

Associate Professor
HKU Musketeers Foundation Institute of Data Science and Department of Computer Science, School of Computing and Data Science, HKU
Professor Yingyu Liang is an Associate Professor in the Musketeers Foundation Institute of Data Science and Department of Computer Science at The University of Hong Kong. He is also an Associate Professor at the Department of Computer Sciences at the University of Wisconsin-Madison. Before that, he was a postdoc at Princeton University. He received his Ph.D. in 2014 from Georgia Tech, and M.S. (2010) and B.S. (2008) from Tsinghua University. He is a recipient of the NSF CAREER award. His research group aims at providing theoretical foundations for modern machine learning models and designing efficient algorithms for real world applications. Recent focuses include optimization and generalization in deep learning, robust machine learning, and their applications.

Professor Difan ZOU

Assistant Professor
HKU Musketeers Foundation Institute of Data Science and Department of Computer Science, School of Computing and Data Science, HKU

Professor Difan Zou is an Assistant Professor in HKU IDS & Computer Science, School of Computing and Data Science, at The University of Hong Kong. He received his Ph.D. in Computer Science, University of California, Los Angeles (UCLA). He received a B. S degree in Applied Physics, from School of Gifted Young, USTC and a M. S degree in Electrical Engineering from USTC. He has published multiple papers on top-tier machine learning conferences including ICML, NeurIPS, ICLR, COLT, etc. He is a recipient of Bloomberg Data Science Ph.D. fellowship. His research interests are broadly in machine learning, optimization, and learning structured data (e.g., time-series or graph data), with a focus on theoretical understanding of the optimization and generalization in deep learning problems.

Dr Yue XIE

Research Assistant Professor
HKU Musketeers Foundation Institute of Data Science and Department of Mathematics, HKU

Dr. Yue Xie is a Research Assistant Professor in Musketeers Foundation Institute of Data Science (HKU-IDS) and Department of Mathematics at the University of Hong Kong. He was a postdoc at UW Madison working in the nonconvex optimization group led by Professor Stephen J. Wright. He received his PhD degree in Pennsylvania State University and Bachelor degree from Tsinghua University. Dr. Yue Xie has been focusing on algorithm design and analysis to address nonconvex and stochastic optimization problems with all types of applications including machine learning and data science. He has published/served as the referee of top-tier journals including Mathematical Programming, SIAM Journal on Optimization, and IEEE Transactions on Automatic Control, etc. He has delivered numerous presentations at major international conferences such as International Conference on Continuous Optimization (ICCOPT), International Symposium on Mathematical Programming (ISMP), SIAM Conference on Optimization and International Conference on Machine Learning (ICML).

Course Description

This course aims to equip the students with fundamental mathematical tools frequently used in data science and prepare them for more advanced study in various directions of data science. It is designed for students who have basic knowledge of linear algebra, calculus, and probability (e.g., undergraduate courses in these topics) and would like later to pursue an in-depth investigation of data science.

For this goal, the course will cover fundamental mathematical tools for data science and focus particularly on their connections to data science. Topics include basic concepts in probability/statistics, linear algebra, and optimization, such as MLE/MAP, elementary information theory, concentration, spectral decomposition, convexity, gradient descent, etc. These are illustrated with the corresponding examples in data science, such as statistical learning, PCA, SGD on empirical loss, etc.

Prerequisites 

Basic knowledge of linear algebra, calculus, and probability (e.g., undergraduate courses in these topics) is recommended. The course is open to beginning graduates with the required math background.