# Mathematical Data Science

Lele Wang (University of British Columbia)Jan 1, 2021 — Jun 1, 2021

## About the course

A large variety of data science and machine learning problems use graphs to characterize the structural properties of the data. In social networks, graphs represent friendship among users. In biological networks, graphs indicate protein interactions. In the World Wide Web, graphs describe hyperlinks between web pages. In recommendation systems, graphs reveal the economic behaviors of users. Unlike the one-dimensional linear data sequence, data appearing in the form of a graph can be viewed as a two-dimensional matrix with special structures. How to compress, store, process, estimate, predict, and learn such large-scale structural information are important new challenges in data science. This course will provide an introduction to mathematical and algorithmic tools for studying such problems. Both information-theoretic methods for determining the fundamental limits as well as methodologies for attaining these limits will be discussed. The course aims to expose students to the state- of-the-art research in mathematical data science, statistical inference on graphs, combinatorial statistics, among others, and prepare them with related research skills.

# Registration

This course is available for registration under the Western Dean's Agreement. To register, you must obtain the approval of the course instructor and you must complete the Western Dean's agreement form , using the details below. The completed form should be signed by your home institution department and school of graduate studies, then returned to the host institution of the course.

## Enrollment Details

- Course Name
- Mathematical Data Science
- Date
- Jan 1, 2021 — Jun 1, 2021
- Course Number
- EECE 571W
- Section Number
- 202
- Section Code

## Instructor(s)

For help with completing the Western Dean’s agreement form, please contact the graduate student program coordinator at your institution. For more information about the agreement, please see the Western Dean's Agreement website

# Other Course Details

### Textbooks

All ebooks are available at https://www.library.ubc.ca/.

- Alan Frieze and Michał Karon ́ ski, Introduction to Random Graphs, Cambridge University Press, 2015
- Béla Bollobás, Random Graphs, 2nd Edition, Cambridge University Press, 2001.
- Svante Janson, Tomasz Łuczak, and Andrzej Rucinski, Random Graphs, John Wiley & Sons, Inc., 2000.
- Noga Alon and Joel H. Spencer, The Probabilistic Method, 4th Edition, Wiley, 2016.

### Assessment scheme

**Grading**: Homework 50% and paper reading 50% (presentations 20%, critical reviews 15%, in-class participation in discussing the paper 15%).**Homework assignment**: In the first half of the course, homework will be assigned every other week on Tuesday and due the Tuesday in two weeks. You are allowed, even encouraged, to work on the homework in small groups, but you must write up your own homework to hand in.**If you use materials other than the textbooks and lecture notes — this applies to having discussions with classmates or searching the Internet — please acknowledge the source clearly.****Paper reading seminar**: The second half of the course will be paper reading seminars. One research paper will be discussed per lecture. Students work in groups. One group is responsible in thoroughly understanding the paper and giving a 40 min summary in class. Remaining groups write critical reviews of the paper before the lecture. Each lecture, there will be a presentation around an hour (40 min technical summary with questions during the presentation), followed by a 20 min discussion about limitations, comparisons, potential improvements, future directions of the paper.- Paper list and assignment will be provided.
- Depending on registration numbers, each group presents 1 paper and writes critical reviews for the remaining papers (one review per group per paper). Guidance on how to structure a presentation and how to review a paper will be provided.
- The presenting group is required to meet the instructor during office hour (or by appointment) to discuss the planned presentation at least two weeks before the lecture.
- Both the presenting group and the reviewing groups should attend the paper reading seminars.