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Mathematics for Data Science (数据中的数学) |
Course Information |
This course is open to graduates and senior undergraduates in applied mathematics and statistics who are involved in dealing with data. It covers some topics on high
dimensional statistics, manifold learning, diffusion geometry, random walks on graphs, concentration of measure, random matrix theory, geometric and topological methods, etc.
Prerequisite: linear algebra, basic probability and multivariate statistics, basic stochastic process (Markov chains).
Tue 10:10-12:00pm;
Fri (odd weeks) 10:10-12:00pm
(Possibly change later!) Rm 425, Ying Jie Exchange Center; 数院本科生机房, 英杰交流中心 425
We are targeting bi-weekly homeworks with mini-projects, and a final major project. No final exam. Scribers will get bonus credit for their wonderful work!
YAN, Bowei (闫博巍) Email: bwyan (add "AT pku DOT edu DOT cn" afterwards)
Date | Topic | Instructor | Scriber |
09/06/2011, Tue | Lecture 01: Introduction: Data Representation, Sample Mean, Variance, and PCA [lecture note 1.pdf]
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Y.Y. | Yan, Bowei |
09/09/2011, Fri | Lecture 02: Stein's Phenomenon and Shrinkage [lecture note 2 by Sheng,Hu.pdf]
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Y.Y. | Sheng, Hu. Luo, Wulin. Lv, Yuan. |
09/13/2011, Tue | Lecture 03: Random Matrix Theory and PCA [lecture note 3.pdf]
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Y.Y. | Tengyuan Liang; Bowei Yan |
09/20/2011, Tue | Lecture 04: Diffusion Map, an introduction [lecture note 4.pdf, version 2]
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Xiuyuan Cheng Princeton |
Peng Luo; Wei Jin |
09/23/2011, Fri | Lecture 05: Diffusion Map, convergence theory [lecture note 5.pdf, version 4]
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Xiuyuan Cheng Princeton |
Jun Yin; Ya'ning Liu |
09/27/2011, Tue | Lecture 06: Diffusion Distance [lecture note 6.pdf]
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Y.Y. | Lei Huang; Yue Zhao |
10/11/2011, Tue | Lecture 07: Random Walk on Graphs: Perron-Frobenius Vector and PageRank [lecture note 7.pdf]
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Y.Y. | Yuan Lu; Bowei Yan |
10/18/2011, Tue | Lecture 08: Random Walk on Graphs: Fiedler Vector, Cheeger inequality and spectral bipartition [lecture note 8.pdf]
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Y.Y. | Zhiming Wang; Feng Lin |
10/21/2011, Fri | Lecture 9: Random Walk on Graphs: Lumpability (metastability), piecewise constant right Eigenvectors and Multiple Spectral Clustering (MNcut) [lecture note 9.pdf]
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Y.Y. | Hong Cheng; Ping Qin |
10/25/2011, Tue | Lecture 10: Random Walk on Graphs: Diffusion Distance and Commute Time Distance [lecture note 10.pdf]
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Y.Y. | Tangjie Lv; Longlong Jiang |
11/01/2011, Tue | Lecture 11: PCA vs. MDS: Schoenberg Theory
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Y.Y. | Yanzhen Deng; Jie Ren |
11/04/2011, Fri | Lecture 12: Random Projections and Metric: Johnson-Lindenstrauss Theory
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Y.Y. | |
11/08/2011, Tue | Lecture 13: MDS with uncertainty: Graph Realization
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Y.Y. | |
11/15/2011, Tue | Lecture 14: Manifold Learning (Nonlinear Dimensionality Reduction): ISOMAP vs. LLE
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Y.Y. | |
11/18/2011, Fri | Lecture 15: Other Manifold Learning Techniques: Laplacian, Hessian, LTSA
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Y.Y. | |
11/22/2011, Tue | Lecture 16: Multiscale SVD and Wavelets on Graphs
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Y.Y. | |
11/29/2011, Tue | Lecture 17: Sparsity in High Dimensional Statistics
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Y.Y. | |
12/02/2011, Fri | Lecture 18:
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Weinan E | |
12/06/2011, Tue | Lecture 19:
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Weinan E | |
12/13/2011, Tue | Lecture 20:
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Y.Y. | |
12/16/2011, Fri | Lecture 21:
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Y.Y. | |
12/20/2011, Tue | Lecture 22: Final Project Report
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Y.Y. |