Math 4803, Fall 2019

Instructor:        Wenjing Liao
Office:              Skiles 258
Email:              wliao60@gatech.edu
Lectures:      M W 4:30-5:45pm, Clough 131
Office Hours:   Tuesday 1-4PM or by appointment
Course webpage: http://people.math.gatech.edu/~wliao60/19Fall_Math4803.html

General course information

Prerequisites: Calculus I and II: Math 1551 and Math 1552; and Linear algebra, such as 1553 or 1554 or 1564
Course description
Course goals:

Introduce modern data science techniques and the foundational mathematical concepts in linear algebra, probability, and basic optimization related with these techniques
Teach how to use software to perform learning tasks while adequately addressing the practical challenges (e.g., modeling, parameter tuning, computation and speed)
Provide students with valuable first-hand experience in handling real and complex data

Textbook and references:

Review of linear algebra: http://cs229.stanford.edu/summer2019/cs229-linalg.pdf
Basic concepts in probability: http://cs229.stanford.edu/summer2019/cs229-prob.pdf
Statistical learning book: James, Gareth, Daniela Witten, Trevor Hastie and Robert Tibshirani, An introduction to statistical learning. Vol. 112, New York: Springer, 2013: http://faculty.marshall.usc.edu/gareth-james/ISL/
Elements of statistical learning: https://web.stanford.edu/~hastie/ElemStatLearn/
Von Luxburg, Ulrike, "A tutorial on spectral clustering" Statistics and computing 17.4, 395-416, 2007.

Tentative topics (may not be all covered):

Chapter 2 of the statistical learning book: introduction to regression, classification and clustering.
Chapter 3 of the statistical learning book: linear regression.
Chapter 4 of the statistical learning book: classification, including logistic regression and linear discriminate analysis.
Chapter 5 of the statistical learning book: resampling methods, especially cross validation.
Chapter 7 of the statistical learning book: moving beyond linearity, including polynomial regression, step functions, regression splines and local regression.
Chapter 10 of the statistical learning book: unsupervised learning, including principal component analysis and K-Means clustering.
Spectral clustering
Multidimensional scaling

Grading:

Grading will be based on exams, homework assignments and a final project: Homework 40% Midterm 20% Final project 40%
There will be 5 homework assignments. The lowest HW score will be dropped.
Midterm is on October 7.
Final project: Students form a group of 3 or 4 to work on a project with real data sets. Groups are expected to be formed no later than Oct 23. The instructor will provide a list of possible projects. Each group will pick a topic by the end of October, and then write a project proposal. The main work of the project is expected to be completed in November. Each group will make a poster and present it in the last lecture on Dec 2.
The course grade will be determined by an absolute scale with a slight modification using the normal distribution curve if appropriate.

General policies:

Calculators are not allowed in exams.
Attendance: Attendance at all lectures is required. If you miss a lecture, it is your responsibility to catch up on the topics that you missed.
If a student is found responsible through the Office of Student Integrity for academic dishonesty on a graded item in this course, the student will receive a score of zero for that assignment, and the final grade for the course will be further reduced by one letter grade.
In this course, as in many math courses, working in groups to study particular problems and discussing theory is strongly encouraged. Your ability to talk mathematics is of particular importance to your general understanding of mathematics. You can discuss with other students about how to approach the problem. However, you must write up the solutions and the programs to the homework problems individually and separately.

Programming: You can choose to use Matlab, Python or R for programming.

Matlab

Python

Homework:
HW 1 due on Wednesday September 4
HW 2 due on Wednesday September 18
HW 3 Part I is due on Wednesday October 2 and Part II is due on Friday October 11
HW 4 due on Monday November 25

Exams:
Midterm 1: covers materials from Week 1 to Week 5

Course Progress:

Week 1

Chapter 1 and 2: Introduction and basis concepts, lecture slides
Chapter 3: Linear regression
Review of linear algebra, lecture notes

Week 2

Chapter 3: Linear regression, lecture slides

Week 3

Review of probability: http://cs229.stanford.edu/summer2019/cs229-prob.pdf

Week 4

Logistic regression, lecture slides
Cross validation, lecture slides

Week 5

Moving beyond linearity, lecture slides

Week 6

Kernel regression, lecture slides

Week 7

Regression and classification trees, lecture slides

Week 8

Support vector machines, lecture slides

Week 9

K means clustering, lecture slides

Week 10

K medoids, lecture slides (at the end)
Review of eigenvalue decomposition of symmetric matrices

Week 11

Principal Component Analysis (PCA)

PCA for faces: https://www.cs.toronto.edu/~guerzhoy/320/lec/pca.pdf

Week 12

PCA from the textbook, slides
Theory of PCA, notes
Presentation of project proposal

Week 13

Spectral clustering: https://www.cs.cmu.edu/~aarti/Class/10701/slides/Lecture21_2.pdf
Reference: Von Luxburg, Ulrike, "A tutorial on spectral clustering" Statistics and computing 17.4, 395-416, 2007

Ethics:
The strength of the university depends on academic and personal integrity. In this course, everyone must be honest and truthful. Violations include cheating on exams, plagiarism, improper use of the internet and electronic devices, unauthorized collaboration, alteration of graded assignments, forgery and falsification, lying, facilitating academic dishonesty and unfair competition. Ignorance of these rules is not an excuse.

Special aid:
Students with disabilities or other special needs that require classroom accommodation or other arrangements must let the instructor know at the beginning of the semester.