# Multivariate Statistics and Machine Learning

*MATH38161*

Lecture Notes

Lecture Notes

*Korbinian Strimmer*

University of Manchester

University of Manchester

*15 November 2020*

# Preface

## About these notes

This is the course text for MATH38161, an introductory course in **Multivariate Statistics and Machine Learning** for third year mathematics students.

These notes will be updated from time to time. To view the current version in your browser visit the online MATH38161 lecture notes. You may also download the MATH38161 lecture notes as PDF.

## About the module

### Topics covered

The MATH38161 module is designed to run over the course of 11 weeks. It has six parts, each covering a particular aspect of multivariate statistics and machine learning:

- Multivariate random variables and estimation in large and small sample settings (W1 and W2)
- Transformations and dimension reduction (W3 and W4)
- Unsupervised learning/clustering (W5 and W6)
- Supervised learning/classification (W7 and W8)
- Measuring and modelling multivariate dependencies (W9)
- Nonlinear and nonparametric models (W10, W11)

This module focuses on:

*Concepts and methods*(not on theory)*Implementation and application in R**Practical data analysis and interpretation*(incl. report writing)*Modern tools in data science and statistics*(R markdown, R studio)

### Additional support material

Accompanying these notes are

- a weekly learning plan for an 11 week study period,
- corresponding worksheets with examples (theory and application in R) and solutions in R Markdown,
- lecture videos (visualiser style).

Organisatorical information is available from the course home page and on Blackboard.

If you are a University of Manchester student and enrolled for this module you can find the exam questions of previous years (without solution) as well as the coursework instructions on Blackboard.

Furthermore, there is also an MATH38161 online reading list hosted by the University of Manchester library.

## Acknowledgements

Many thanks to Beatriz Costa Gomes for her help to compile the first draft of these course notes in the winter term 2018 while she was a graduate teaching assistant for this course. I also thank the many students who suggested corrections.