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Taiwan Mathematics School: Mathematical foundation toward artificial intelligence in medicine
13:20-15:10, every Tuesday and Thursday , February 23 - June 17, 2021
R305, Astronomy-Mathematics Building, NTU

Hau-Tieng Wu (Duke University)

Hau-Tieng Wu (Duke University)

Course Description
Advances in technology have led to versatile and complicated modern datasets, particularly at the forefront of medical advances. With modern data analysis, it has been claimed that soon artificial intelligence (AI) would be generated and human being will be replaced. Toward this goal, the main question is how to analyze modern datasets.
Nonlinearity and nonstationarity are common features of these modern datasets. To quantify these features and hence carry out statistical analyses, there are unprecedented demand for new techniques to model the underlying structure, and develop algorithms to analyze the data. On the other hand, a solid and correct understanding of background knowledge plays a significant role when we apply these new techniques, particularly for the scientific research purpose.
In this lecture, we focus on modern machine learning techniques, particularly unsupervised learning, from both theoretical and practical perspectives, and aim for solving real-world biomedical problems, and hence a possibly ideal AI, or intelligence augment (IA) system. This course is designed to train simultaneously students from different and diverse disciplines with proper background (shown below), including but not exclusively mathematics, statistics, engineering and medicine.
1. From the theoretical perspective, we introduce statistical theories established based on the differential geometry and random matrix theory framework. We will focus on feature extraction, dimension reduction, data visualization, etc. All introduced theories are needed for real world problems.
2. From the algorithmic perspective, we will provide algorithm details and implementation tricks. Matlab code will be provided for practicing.
3. From the practical perspective, we will discuss how to apply the introduced algorithms and established theory to analyze real datasets assuming basic knowledge of supervised learning tools. Wewill focus on extracting dynamics from biomedical time series, either single channel and multiple channels. We will not focus on biomedical image analysis or pattern recognition unless the temporal information is a concern in the dataset.
Students will be formed into groups, and each group will be assigned a medical problem, a physician mentor, and a hospital. Minimally two hospital tours will be arranged for students to appreciate the importance of clinical problems, and how the data collection and analysis result application are carried out in the clinical environment. Fully/partially solving this medical problem with mathematically rigorous techniques is the goal of this course.
A short summary course of needed background on several topics will be provided in the format of seminar discussion before the semester starts for the sake of self-containedness. Due to the black-box nature of deep learning and the dangers of abuse, it is not the focus of this lecture.


Contact: murphyyu@ncts.ntu.edu.tw

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