Data Analysis and Matrix Computations
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数据分析与矩阵计算课程将提供线性代数、概率统计、优化、矩阵计算、编程等方面的训练，为开展在数据科学、机器学习、信号处理等领域的学习和研究奠定一定的基础。 |
Prerequisites: Mathematical Analysis, Advanced Algebra, Probability, Numerical Linear Algebra
Highlights: 教研结合型课程
Grading Policy: Classroom performance & Assignments 60% + Final exam 40%
Instructor
Kui Du, Email: kuidu@xmu.edu.cn Office: B603 Math Building, Haiyun Campus
References
The Mathematics of Data, Editors: Michael W. Mahoney, John C. Duchi, and Anna C. Gilbert, AMS, IAS, SIAM, 2018
Bayesian Scientific Computing, Daniela Calvetti and Erkki Somersalo, Springer, 2023
Randomized matrix computations: Themes and variations, Anastasia Kireeva and Joel A. Tropp, arXiv:2402.17873, 2024
Introduction to Nonlinear Optimization: Theory, Algorithms, and Applications with Python and MATLAB, Amir Beck, 2nd Edition, SIAM, 2023
Mathematics of Data Science: A Computational Approach to Clustering and Classification, Daniela Calvetti and Erkki Somersalo, SIAM, 2021
Mathematics for Machine Learning, Marc Peter Deisenroth, A. Aldo Faisal, and Cheng Soon Ong, Cambridge University Press, 2020
Lecture Notes (tentative)
Lecture 1: Fundamentals of probability
Lecture 2: Randomized iterative methods for linear systems
Lecture 3: Low-rank matrix approximation
Lecture 4: Randomized linear dimension reduction
Lecture 5: Unconstrained optimization
Lecture 6: Convex sets and convex functions
Lecture 7: Constrained optimization
Lecture 8: Support vector machine
Assignments (tentative)
Other
High-Dimensional Data Analysis with Low-Dimensional Models: Principles, Computation, and Applications, John Wright and Yi Ma, Cambridge University Press, 2022
High-Dimensional Probability: An Introduction with Applications in Data Science, Roman Vershynin, Cambridge University Press, 2018
First-Order Methods in Optimization, Amir Beck, SIAM, 2017
Numerical Optimization, Jorge Nocedal and Stephen J. Wright, Second Edition, Springer, 2006
Convex Optimization, Stephen Boyd and Lieven Vandenberghe, Cambridge University Press, 2004