This research-led course provides an introduction to recent developments in Random Matrix Theory and Online Learning that addresses the challenges and opportunities posed by the availability of large amounts of data.

In the first instance, we will review some classic results from multivariate statistical theory, matrix analysis, and probability theory. Then we will present the salient statistical features of big data (e.g., heterogeneity, noise accumulation, spurious correlation, and incidental endogeneity) and show how this impacts on traditional statistical methods and theory.

We follow with an introduction to modern Random Matrix theory and its application in statistics. Applications presented may include topics such as high-dimensional statistical inference, large covariance matrices, large-scale statistical learning through subsampling, sparsification of large matrices, principal component analysis, and dimension reduction.

We conclude with an introduction to the theory of online learning (aka. sequential prediction) to handle the situation of streaming data.

Students will use and learn about the latest computational tools to work with big and streaming data sets. Example data sets may be drawn from areas such finance, web analytics, digital marketing, and satellite imagery data.

Learning Outcomes

Upon successful completion, students will have the knowledge and skills to:

1. Explain how statistical features of big data impact traditional statistical methods and theory.
2. Discuss Random Matrix theory and its application in statistics on large scale.
3. Summarise the theory of sequential prediction and management of streaming data.
4. Demonstrate the use of computational tools to work with big and streaming data sets.

Research-Led Teaching

This course introduces statistical inference on big data with techniques from large-dimensional random matrix theory, as well as applications in large portfolio theory (Finance) and insurance pricing (Actuarial Science). This course is based on recent research papers from Statistics, Finance and Actuarial Science. The topic is rapidly advancing and recent results may be introduced into the course as they appear in the literature.  

Examination Material or equipment

R software

Required Resources

R (free to download)

The course makes extensive use of the free R software for statistical computing. PC/Mac labs are located at many places around campus: for an exhaustive list, visit the Information Commons link at

https://services.anu.edu.au/information-technology/software-systems

Students should be able to use their student cards to access these computing laboratories and should have a computer account automatically set up for them upon registration for this course. If you have not registered for the course, your card will not allow you access to the lab. To get started with the computing requirements for the course, students should make sure that they read the document "Introductory R Worksheet 1: PC familiarity" (linked to from the R workshop page, a link to which appears on the class home page). This document describes how you can log in to the PC’s. This document will also tell you how you can obtain or view other documents that you will find useful to learn about the computing setup for the course.

From the web page, you will be able to print out all of the lecture notes, all of the computer code used in the class, and all the tutorials and solutions.

No handouts will be made available except on the class web page.

A number of data sets will be analysed during lectures, live using R as much as possible. To assist you in understanding the data analyses, the R code used to produce displays discussed in class will be made available to you on the class web page. You are free to use and modify this code in conducting your own analyses.

Lecture Notes (available on Canvas). Class materials, including detailed lecture notes, workshop materials, tutorials, assignments and other relevant materials, will be made available on the class web page hosted on Canvas at https://canvas.anu.edu.au . To log on to Canvas, you need to have an ANU ID (your student number) and a password (the same as for obtaining your e-mail). In order to access the class web page within Canvas, you will need to be formally enrolled in the course. The class web page will be updated with new information on a regular basis, and will also contain links to other places of interest (such as an R workshop initially). It is essential that you visit the class web page regularly.

Reference materials

Resources (research papers, etc) and lecture notes will be provided throughout the semester on Canvas.

Staff Feedback

Students will be given feedback in the following forms in this course:

• Written comments
• Verbal comments
• Feedback to the whole class, to groups, to individuals, focus groups

Student Feedback

ANU is committed to the demonstration of educational excellence and regularly seeks feedback from students. Students are encouraged to offer feedback directly to their Course Convener or through their College and Course representatives (if applicable). The feedback given in these surveys is anonymous and provides the Colleges, University Education Committee and Academic Board with opportunities to recognise excellent teaching, and opportunities for improvement. The Surveys and Evaluation website provides more information on student surveys at ANU and reports on the feedback provided on ANU courses.

Class Schedule

Week/Session	Summary of Activities	Assessment
1	Topic: Introduction to Big Data Challenges and Overview of the CourseActivity: Lecture/Workshop Reading: Lecture Note 1
2	Topic: Preliminary Knowledge (Matrix Analysis, Eigenvalues and Eigenvectors, Multivariate Normal Distribution)Activity: Lecture/Workshop/Tutorial (Tutorial 1 Questions)Reading: Lecture Note 2 / Workshop Material 1
3	Topic: Introduction to Large-dimensional Random Matrix Theory (Limiting Spectral Distribution, Marcenko-Pastur Distribution, Fisher Spectral Distribution)Activity: Lecture/Workshop/Tutorial (Tutorial 2 Questions)Reading: Lecture Note 3 / Workshop Material 2	Assessment 1 Due (8 August 4:00pm)
4	Topic: Linear Spectral Statistics and its Asymptotic PropertiesActivity: Lecture/Workshop/Tutorial (Tutorial 3 Questions)Reading: Lecture Note 4 / Workshop Material 3
5	Topic: Big Data Analysis in Finance - Large Portfolio SelectionActivity: Lecture/Workshop/Tutorial (Tutorial 4 Questions)Reading: Lecture Note 5 / Workshop Material 4
6	Topic: Eigen-Analysis of Large-dimensional Sample Covariance MatrixActivity: Lecture/Workshop/Tutorial (Tutorial 5 Questions)Reading: Lecture Note 6 / Workshop Material 5	Assessment 2 Due (29 August 4:00pm)
7	Topic: Generalised Variance in High DimensionsActivity: Lecture/Workshop/Tutorial (Tutorial 6 Questions)Reading: Lecture Note 7 / Workshop Material 6
8	Topic: Principal Component Analysis for Big DataActivity: Lecture/Workshop/Tutorial (Tutorial 7 Questions)Reading: Lecture Note 8 / Workshop Material 7
9	Topic: Big Data Analysis in Actuarial Science - Age-specific Mortality ForecastingActivity: Lecture/Workshop/Tutorial (Tutorial 8 Questions)Reading: Lecture Note 9 / Workshop Material 8	Assessment 3 Due (3 October 4:00pm)
10	Topic: Canonical Correlation Analysis for Multi-population Big DataActivity: Lecture/Workshop/Tutorial (Tutorial 9 Questions)Reading: Lecture Note 10 / Workshop Material 9
11	Topic: Eigen-analysis for Complex Matrix Data (Spurious Factor Analysis and Application)Activity: Lecture/Workshop/Tutorial (Tutorial 10 Questions)Reading: Lecture Note 11/ Workshop Material 10
12	Topic: Linear Regression for Big Matrix DataActivity: Lecture/Workshop/Tutorial (Tutorial 11 Questions)Reading: Lecture Note 12 / Workshop Material 11	Final Project Due (30 October 4:00pm)

Tutorial Registration

Tutorials commence in Week 2 of the semester and will be held on campus. ANU utilises MyTimetable to enable students to view the timetable for their enrolled courses, browse, then self-allocate to small teaching activities / tutorials so they can better plan their time. Find out more on the Timetable webpage (https://www.anu.edu.au/students/program-administration/timetabling).

Assessment Summary

Assessment task	Value	Due Date	Return of assessment	Learning Outcomes
Assessment 1	25 %	08/08/2025	22/08/2025	1,2
Assessment 2	25 %	29/08/2025	12/09/2025	1,2,3
Assessment 3	25 %	03/10/2025	17/10/2025	1,2,3,4
Final Project	25 %	30/10/2025	27/11/2025	1,2,3,4

* If the Due Date and Return of Assessment date are blank, see the Assessment Tab for specific Assessment Task details

Policies

ANU has educational policies, procedures and guidelines, which are designed to ensure that staff and students are aware of the University’s academic standards, and implement them. Students are expected to have read the Academic Misconduct Rule before the commencement of their course. Other key policies and guidelines include:

• Student Assessment (Coursework) Policy and Procedure
• Special Assessment Consideration Policy and General Information
• Student Surveys and Evaluations
• Deferred Examinations
• Student Complaint Resolution Policy and Procedure

Assessment Requirements

The ANU is using Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. For additional information regarding Turnitin please visit the ANU Online website Students may choose not to submit assessment items through Turnitin. In this instance you will be required to submit, alongside the assessment item itself, hard copies of all references included in the assessment item.

Moderation of Assessment

Marks that are allocated during Semester are to be considered provisional until formalised by the College examiners meeting at the end of each Semester. If appropriate, some moderation of marks might be applied prior to final results being released.

Participation

This course has 4 hours of contact time per week, this consists of:

(a) In-person weekly lectures where the theory material is covered (2 hours). These lectures will be held on campus and recorded.

(b) A 1 hour weekly workshop where applications and illustrations of the theory are demonstrated. This will be a live RStudio session.

(c) A weekly tutorial held in a computer lab (1 hour) where you get the opportunity to practice what you have learnt.

Students are encouraged to attend all of these sessions on a weekly basis to take notes and ask questions.

Examination(s)

There is no final examination for this course. The final assessment is a take-home project (Assessment Task 4).

Assessment Task 1

Assessment 1

This assessment is to be done individually. This assessment will be a take-home assessment that will typically involve a mix of ‘pen-and-paper’ questions and/or ‘computational’ questions. This assessment will match the style of questions given in the tutorials, so practicing on those questions would be quite beneficial. The question(s) will cover material that has been seen in previous lectures and are aimed at ensuring students are routinely studying the material. The assessment will be released two weeks before the due date. The assessment will be submitted in Canvas using TurnitIn by 4:00pm on the due date and marks/feedback will be given on the 'Return of Assessment Date'.

Assessment Task 2

Assessment 2

This assessment is to be done individually. This assessment will be a take-home assessment that will typically involve a mix of ‘pen-and-paper’ questions and/or ‘computational’ questions. This assessment will match the style of questions given in the tutorials, so practicing on those questions would be quite beneficial. The question(s) will cover material that has been seen in previous lectures and are aimed at ensuring students are routinely studying the material. The assessment will be released two weeks before the due date. The assessment will be submitted in Canvas using TurnitIn by 4:00pm on the due date and marks/feedback will be given on the 'Return of Assessment Date'.

Assessment Task 3

Assessment 3

This assessment is to be done individually. This assessment will be a take-home assessment that will typically involve a mix of ‘pen-and-paper’ questions and/or ‘computational’ questions. This assessment will match the style of questions given in the tutorials, so practicing on those questions would be quite beneficial. The question(s) will cover material that has been seen in previous lectures and are aimed at ensuring students are routinely studying the material. The assessment will be released two weeks before the due date. The assessment will be submitted in Canvas using TurnitIn by 4:00pm on the due date and marks/feedback will be given on the 'Return of Assessment Date'.

Assessment Task 4

Final Project

This assessment is to be done individually. This assessment will be a take-home assessment that will typically involve a mix of ‘pen-and-paper’ questions and/or ‘computational’ questions. This assessment will match the style of questions given in the tutorials, so practicing on those questions would be quite beneficial. The question(s) will cover material that has been seen in previous lectures and are aimed at ensuring students are routinely studying the material. The assessment will be released two weeks before the due date. The assessment will be submitted in Canvas using TurnitIn by 4:00pm on the due date and marks will be given on the day of release of final results (27 Nov 2025).

Academic Integrity

Academic integrity is a core part of our culture as a community of scholars. At its heart, academic integrity is about behaving ethically. This means that all members of the community commit to honest and responsible scholarly practice and to upholding these values with respect and fairness. The Australian National University commits to embedding the values of academic integrity in our teaching and learning. We ensure that all members of our community understand how to engage in academic work in ways that are consistent with, and actively support academic integrity. The ANU expects staff and students to uphold high standards of academic integrity and act ethically and honestly, to ensure the quality and value of the qualification that you will graduate with. The University has policies and procedures in place to promote academic integrity and manage academic misconduct. Visit the following Academic honesty & plagiarism website for more information about academic integrity and what the ANU considers academic misconduct. The ANU offers a number of services to assist students with their assignments, examinations, and other learning activities. The Academic Skills and Learning Centre offers a number of workshops and seminars that you may find useful for your studies.

Online Submission

The ANU uses Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. The use of Turnitin is mandatory without an exemption. Any student identified, either during the current semester or in retrospect, as having used ghost writing services will be investigated under the University’s Academic Misconduct Rule. The assignments and final project must be done individually, any similarities between results will be investigated under the University’s Academic Misconduct Rule.

 

Hardcopy Submission

All assessment submission in the course is online.

Late Submission

Late submission of assignments will incur a penalty of 5% per working day. Further, any late assessment tasks will not to be accepted after the earlier of the following: (1) The tenth working day after the due date; or, (2) The date specified in the class summary for the return of the assessment item.

Referencing Requirements

Accepted academic practice for referencing sources that you use in presentations can be found via the links on the Wattle site, under the file named “ANU and College Policies, Program Information, Student Support Services and Assessment”. Alternatively, you can seek help through the Students Learning Development website.

Returning Assignments

Assignments will be graded and returned on Canvas via TurnitIn. Students are encouraged to use the consultation time of the tutor and lecturer to obtain further feedback if necessary.

Extensions and Penalties

Extensions and late submission of assessment pieces are covered by the Student Assessment (Coursework) Policy and Procedure The Course Convener may grant extensions for assessment pieces that are not examinations or take-home examinations. If you need an extension, you must request an extension in writing on or before the due date. If you have documented and appropriate medical evidence that demonstrates you were not able to request an extension on or before the due date, you may be able to request it after the due date.

Resubmission of Assignments

Not applicable.

Privacy Notice

The ANU has made a number of third party, online, databases available for students to use. Use of each online database is conditional on student end users first agreeing to the database licensor’s terms of service and/or privacy policy. Students should read these carefully. In some cases student end users will be required to register an account with the database licensor and submit personal information, including their: first name; last name; ANU email address; and other information. In cases where student end users are asked to submit ‘content’ to a database, such as an assignment or short answers, the database licensor may only use the student’s ‘content’ in accordance with the terms of service — including any (copyright) licence the student grants to the database licensor. Any personal information or content a student submits may be stored by the licensor, potentially offshore, and will be used to process the database service in accordance with the licensors terms of service and/or privacy policy. If any student chooses not to agree to the database licensor’s terms of service or privacy policy, the student will not be able to access and use the database. In these circumstances students should contact their lecturer to enquire about alternative arrangements that are available.

Distribution of grades policy

Academic Quality Assurance Committee monitors the performance of students, including attrition, further study and employment rates and grade distribution, and College reports on quality assurance processes for assessment activities, including alignment with national and international disciplinary and interdisciplinary standards, as well as qualification type learning outcomes. Since first semester 1994, ANU uses a grading scale for all courses. This grading scale is used by all academic areas of the University.

Support for students

The University offers students support through several different services. You may contact the services listed below directly or seek advice from your Course Convener, Student Administrators, or your College and Course representatives (if applicable).

• ANU Health, safety & wellbeing for medical services, counselling, mental health and spiritual support
• ANU Diversity and inclusion for students with a disability or ongoing or chronic illness
• ANU Dean of Students for confidential, impartial advice and help to resolve problems between students and the academic or administrative areas of the University
• ANU Academic Skills and Learning Centre supports you make your own decisions about how you learn and manage your workload.
• ANU Counselling Centre promotes, supports and enhances mental health and wellbeing within the University student community.
• ANUSA supports and represents undergraduate and ANU College students
• PARSA supports and represents postgraduate and research students