PKU

A Mathematical Introduction to Data Science (数据分析的数学导论)
Fall 2014


Course Information

Synopsis (摘要)

This course is open to graduates and senior undergraduates in applied mathematics and statistics who are interested in learning from data. Students with other backgrounds such as engineering and biology are also welcome, provided you have certain maturity of mathematics. 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); familarity with Matlab or R.
Note: the website was broken due to a recent collapse of math.pku.edu.cn server and is still under recovery...

Lecture Notes (constantly updated)

[pdf download]

Time and Place:

Tuesday 6:40-9:30pm;
The 3rd Lecture Hall (三教) Rm 403
eBanshu classroom

Homework and Projects:

We are targeting weekly homeworks with monthly mini-projects, and a final major project. No final exam. Scribers will get bonus credit for their work!

Teaching Assistant (助教):

XIONG, Jiechao (熊杰超) Email: datascience_hw (add "AT 126 DOT com" afterwards)

Schedule (时间表)

Date Topic Instructor Scriber
09/16/2013, Tue Lecture 01: Introduction to Course Syllabus [pdf]
Yuan Yao
09/23/2013, Tue Lecture 02: MDS and PCA [pdf]
    [Homework 1]:
  • Homework 1 [pdf]. Deadline: 09/30/2014, Tuesday. Mark on the head of your homework: Name - Student ID.
Yuan Yao
09/30/2013, Tue Lecture 03: Random Projections [pdf]
    [Homework 2]:
  • Homework 2 [pdf]. Deadline: 10/14/2014, Tuesday. Mark on the head of your homework: Name - Student ID.
Yuan Yao
10/14/2013, Tue Lecture 04: Stein's Phenomenon [pdf]
Yuan Yao
10/21/2012, Tue Lecture 05: Manifold Learning (Nonlinear Dimensionality Reduction): ISOMAP vs. LLE [slides]
    [Reference]:
  • [ISOMAP]: a science (2000) paper on MDS with geodesic distance (graph shortest path distance);
  • [LLE]: a science (2000) paper on Locally Linear Embedding, i.e. local pca (complement) with global alignment;
    [Homework 4]:
  • Homework 4 [pdf]. Deadline: 10/28/2014, Tuesday. Mark on the head of your homework: Name - Student ID.
Yuan Yao
10/28/2012, Tue Lecture 06: Manifold Learning (Nonlinear Dimensionality Reduction): LLE extensions [slides]
    [Reference]:
  • [Laplacian]: Laplacian Eigenmap (LLE) by Misha Belkin and Partha Niyogi 2003;
  • [Hessian]: Hessian Eigenmap (LLE) by David Donoho and Carrie Grimes 2003;
  • [LTSA]: Local Tangent Space Alignment by Hongyuan Zha and Zhenyue Zhang 2005;
  • [Hein05]: consistency of Laplacian Eigenmap
  • [Luxburg08]: consistency of Spectral Clustering
  • [ZhaZha09]: consistency of LTSA
Yuan Yao
11/2/2012, Sun Lecture 07: Random Matrix Theory for PCA [slides]
Yuan Yao
11/4/2012, Tue Lecture 08: SDP relaxations: Robust PCA and Sparse PCA [slides]
Yuan Yao
11/18/2012, Tue Lecture 09: Random Walks on Graphs I: Perron-Frobenius Theory and Primary Eigenvector [lecture notes]
    [Homework 6]:
  • Homework 6 [pdf]. Deadline: 11/25/2014, Tuesday. Mark on the head of your homework: Name - Student ID.
Yuan Yao
  • Xiaowei Wang
  • Zhimei Ren
  • 11/25/2012, Tue Lecture 10: Random Walks on Graphs II: Cheeger Inequalities and Second Eigenvector [lecture notes]
      [Homework 7]:
    • Homework 7 [pdf]. Deadline: 12/2/2014, Tuesday. Mark on the head of your homework: Name - Student ID.
    Yuan Yao Shaokun LI
    12/2/2012, Tue Lecture 11: Random Walks on Graphs III: Lumpability vs. Multiple Spectral Clustering and Transition Path Theory vs. Semisupervised Learning [lecture notes]
      [Homework 8]:
    • Homework 7 [pdf]. Deadline: 12/7/2014, Tuesday. Mark on the head of your homework: Name - Student ID.
    Yuan Yao
  • Zhimei Ren
  • Xiaowei Wang
  • Yongyi Guo
  • 12/9/2012, Tue Lecture 12: SDP Extension of MDS [lecture notes in ebanshu]
    Yuan Yao
    12/16/2012, Tue Lecture 13: Compressed Sensing and High-Dimensional Statistics [lecture notes]
      [Homework 9]:
    • Homework 9 [pdf]. Deadline: 12/30/2014, Tuesday. Mark on the head of your homework: Name - Student ID.
    Yuan Yao
  • Xiaowei Wang
  • Yongyi Guo
  • Zhimei Ren
  • 12/23/2012, Tue Lecture 14: From Graphs to Complexes: Topological Data Analysis [slides] [lecture notes in Ebanshu]
    Yuan Yao
    12/30/2012, Tue Lecture 15: Applied Hodge Theory in Data Analysis [slides] [lecture notes in Ebanshu]
    Yuan Yao

    Reference


    by YAO, Yuan.