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 in detail how statistical features of big data impacts traditional statistical methods and theory;
2. Discuss in depth random Matrix theory and its application in statistics on large scale;
3. Critically discuss the theory of sequential prediction and management of streaming data; and
4. Demonstrate in detail the use of computational tools to work with big and streaming data sets.

Research-Led Teaching

This course is based on recent research papers and surveys applications of random matrix theory in statistics. The topic is rapidly advancing and recent results may be introduced into the course as they appear in the literature.  

Examination Material or equipment

There is no final examination for this course. The final assessment is a project.

Required Resources

None. Resources (research papers, etc) and lecture notes will be provided throughout the semester.

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). Feedback can also be provided to Course Conveners and teachers via the Student Experience of Learning & Teaching (SELT) feedback program. SELT surveys are confidential and also provide the Colleges and ANU Executive with opportunities to recognise excellent teaching, and opportunities for improvement.

Class Schedule

Week/Session	Summary of Activities	Assessment
1	Introduction to the challenges of Big Data and overview of the course. Review of some prerequisite concepts.
2	Further matrix analysis, eigenvalues and eigenvectors, the multivariate normal distribution.
3	Fundamental tools for studying limiting spectral distributions, Marcenko-Pastur distributions, Fisher spectral distribution.	Assignment 1 Due
4	CLT for linear spectral statistics: Introduction and integration tools.
5	Moments and statistics of the Marcenko-Pastur distribution.
6	CLT for linear spectral statistics: Sample covariance matrix, Bai and Silverstein’s CLT, CLT for random Fisher matrices.	Assignment 2 Due
7	Generalised variance in higher dimensions.	Assignment 3 Due
8	Multiple correlation coefficient.
9	Multivariate linear regression in the high-dimensional setting.	Assignment 4 Due
10	PCA and high-dimensional spiked population models.
11	Applications and recent theoretical results.
12	Applications and recent theoretical results.	Assignment 5 Due

Tutorial Registration

There are no regular tutorials for this course.

Assessment Summary

Assessment task	Value	Due Date	Return of assessment	Learning Outcomes
Assignment 1	20 %	08/08/2022	22/08/2022	1-4
Assignment 2	20 %	29/08/2022	12/09/2022	1-4
Assignment 3	20 %	19/09/2022	03/10/2022	1-4
Assignment 4	20 %	04/10/2022	18/10/2022	1-4
Final Project	20 %	03/11/2022	01/12/2022	1-4

* 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 Integrity Rule before the commencement of their course. Other key policies and guidelines include:

• Academic Integrity Policy and Procedure
• 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
• Code of practice for teaching and learning

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 delivered online where applications and illustrations of the theory are demonstrated. This will be a live coding session in RStudio. This workshop will be held live through a scheduled Zoom session with a recording available afterwards.

(c) A weekly tutorial (1 hour) where you get the opportunity to practice what you have learnt.

Examination(s)

There is no final examination for this course. The final assessment is a project.

Assessment Task 1

Assignment 1

This assessment is to be done individually. The assignment will be a take-home assessment that will typically involve a mix of ‘pen-and-paper’ questions and/or a ‘computational’ questions. 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 Wattle using TurnitIn by 9:00am on the due date and marks/feedback will be given on the 'Return of Assessment Date'.

Assessment Task 2

Assignment 2

This assessment is to be done individually. The assignment will be a take-home assessment that will typically involve a mix of ‘pen-and-paper’ questions and/or a ‘computational’ questions. 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 Wattle using TurnitIn by 9:00am on the due date and marks/feedback will be given on the 'Return of Assessment Date'.

Assessment Task 3

Assignment 3

This assessment is to be done individually. The assignment will be a take-home assessment that will typically involve a mix of ‘pen-and-paper’ questions and/or a ‘computational’ questions. 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 Wattle using TurnitIn by 9:00am on the due date and marks/feedback will be given on the 'Return of Assessment Date'.

Assessment Task 4

Assignment 4

This assessment is to be done individually. The assignment will be a take-home assessment that will typically involve a mix of ‘pen-and-paper’ questions and/or a ‘computational’ questions. 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 Wattle using TurnitIn by 9:00am on the due date and marks/feedback will be given on the 'Return of Assessment Date'.

Assessment Task 5

Final Project

This assessment is to be done individually. The final project will be a take-home assessment that will typically involve a mix of ‘pen-and-paper’ questions and/or a ‘computational’ questions. 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 Wattle using TurnitIn by 9:00am on the due date and marks/feedback will be given on the 'Return of Assessment Date'.

Academic Integrity

Academic integrity is a core part of the ANU culture as a community of scholars. The University’s students are an integral part of that community. The academic integrity principle commits all students to engage in academic work in ways that are consistent with, and actively support, academic integrity, and to uphold this commitment by behaving honestly, responsibly and ethically, and with respect and fairness, in scholarly practice.

The University expects all staff and students to be familiar with the academic integrity principle, the Academic Integrity Rule 2021, the Policy: Student Academic Integrity and Procedure: Student Academic Integrity, and to uphold high standards of academic integrity to ensure the quality and value of our qualifications.

The Academic Integrity Rule 2021 is a legal document that the University uses to promote academic integrity, and manage breaches of the academic integrity principle. The Policy and Procedure support the Rule by outlining overarching principles, responsibilities and processes. The Academic Integrity Rule 2021 commences on 1 December 2021 and applies to courses commencing on or after that date, as well as to research conduct occurring on or after that date. Prior to this, the Academic Misconduct Rule 2015 applies.

 

The University commits to assisting all students to understand how to engage in academic work in ways that are consistent with, and actively support academic integrity. All coursework students must complete the online Academic Integrity Module (Epigeum), and Higher Degree Research (HDR) students are required to complete research integrity training. The Academic Integrity website provides information about services available to assist students with their assignments, examinations and other learning activities, as well as understanding and upholding academic integrity.

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 submissions of assessments will occur a penalty of 5% per working day. Assessments 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

The Academic Skills website has information to assist you with your writing and assessments. The website includes information about Academic Integrity including referencing requirements for different disciplines. There is also information on Plagiarism and different ways to use source material.

Returning Assignments

Assignment will be returned online.

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

Assignments may not be resubmitted.

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