DATA8001 - High-Dimensional Data Analysis
Course Instructor
Professor Yi MA
Director, HKU Musketeers Foundation Institute of Data Science
Director, HKU School of Computing and Data Science
Professor, Chair of Artificial Intelligence
Professor Yi Ma is a Chair Professor in the Musketeers Foundation Institute of Data Science (HKU IDS) and Department of Computer Science at the University of Hong Kong. He took up the Directorship of HKU IDS on January 12, 2023. He is also a Professor at the Department of Electrical Engineering and Computer Sciences at the University of California, Berkeley. He has published about 60 journal papers, 120 conference papers, and three textbooks in computer vision, generalized principal component analysis, and high-dimensional data analysis.
Professor Ma's research interests cover computer vision, high-dimensional data analysis, and intelligent systems. For full biography of Professor Ma, please refer to: https://datascience.hku.hk/people/yi-ma/
Course Description
This graduate course introduces basic geometric and statistical concepts and principles of low- dimensional models for high-dimensional signal and data analysis, spanning basic theory, efficient algorithms, and diverse applications. We will discuss recovery theory, based on high-dimensional geometry and non-asymptotic statistics, for sparse, low-rank, and low-dimensional models – including compressed sensing theory, matrix completion, robust principal component analysis, and dictionary learning etc. We will introduce principled methods for developing efficient optimization algorithms for recovering low-dimensional structures, with an emphasis on scalable and efficient first-order methods, for solving the associated convex and nonconvex problems. We will illustrate the theory and algorithms with numerous application examples, drawn from computer vision, im- age processing, audio processing, communications, scientific imaging, bioinformatics, information retrieval etc. The course will provide ample mathematical and programming exercises with sup- porting algorithms, codes, and data. A final course project will give students additional hands-on experience with an application area of their choosing. Throughout the course, we will discuss strong conceptual, algorithmic, and theoretical connections between low-dimensional models with other popular data-driven methods such as deep neural networks (DNNs), providing new perspectives to understand deep learning.
The course includes 3 hours of lectures (by the instructor) and 1 hour discussion session (by a GSI) per week. Homework includes both written exercises and programming exercises. A final course project includes a midterm proposal and final presentation and report.
Prerequisites
We require students to have prior knowledge in undergraduate linear algebra, statistics, and probability. Background in signal processing, optimization, machine learning, and computer vision may allow you to appreciate better certain aspects of the course material, but not necessary all at once.
HKU IDS
Research Postgraduate Programme
DATA8001 - High-Dimensional Data Analysis (Foundation)
Course Instructor
Professor Yi MA
Course Description
This graduate course introduces basic geometric and statistical concepts and principles of low- dimensional models for high-dimensional signal and data analysis, spanning basic theory, efficient algorithms, and diverse applications. We will discuss recovery theory, based on high-dimensional geometry and non-asymptotic statistics, for sparse, low-rank, and low-dimensional models – including compressed sensing theory, matrix completion, robust principal component analysis, and dictionary learning etc. We will introduce principled methods for developing efficient optimization algorithms for recovering low-dimensional structures, with an emphasis on scalable and efficient first-order methods, for solving the associated convex and nonconvex problems. We will illustrate the theory and algorithms with numerous application examples, drawn from computer vision, im- age processing, audio processing, communications, scientific imaging, bioinformatics, information retrieval etc. The course will provide ample mathematical and programming exercises with sup- porting algorithms, codes, and data. A final course project will give students additional hands-on experience with an application area of their choosing. Throughout the course, we will discuss strong conceptual, algorithmic, and theoretical connections between low-dimensional models with other popular data-driven methods such as deep neural networks (DNNs), providing new perspectives to understand deep learning.
The course includes 3 hours of lectures (by the instructor) and 1 hour discussion session (by a GSI) per week. Homework includes both written exercises and programming exercises. A final course project includes a midterm proposal and final presentation and report.
Prerequisites
We require students to have prior knowledge in undergraduate linear algebra, statistics, and probability. Background in signal processing, optimization, machine learning, and computer vision may allow you to appreciate better certain aspects of the course material, but not necessary all at once.