Multivariate Statistics 2

Participants will learn when and how to apply unsupervised and supervised dimension reduction techniques, including MDS, MFA, t-SNE, UMAP, PCR, and PLSR. The lecture will begin with a brief introduction to PCA, while more detailed coverage of PCA is offered in the Multivariate Statistics 1 course. Additionally, the lecture includes a short overview of multi-omics factor analysis (MOFA). The course content is designed to provide a foundational understanding of the theory behind multivariate analysis. Each topic is accompanied by hands-on exercises using the statistical software R. Participants are encouraged to ask questions and seek advice on analyzing their own datasets.

Topics:

This course on multivariate statistics covers two different topics:

• Unsupervised dimension reduction methods: This first chapter starts with a short repetition on the basic principles of principal component analysis (PCA). After this introduction, more advanced dimension reduction techniques are explained, namely multidimensional scaling (MDS) and multiple factor analysis (MFA) for data structured into groups. A brief overview on multi-omics factor analysis (MOFA) is also part of the lecture. This chapter focuses as well on techniques developed for high-dimensional data set (e.g., omics data), namely t-SNE and UMAP.
• Supervised dimension reduction methods: This second chapter covers two supervised learning methods: principal component regression (PCR) and partial least squares regression (PLSR).

Methods:

Each day consists of blocks covering first the theory behind the methods and their applications in R. Theoretical lessons will be followed by hands-on examples with best-practice solutions.

1. Understand and Apply Unsupervised Dimension Reduction Techniques

• Explain the basics of PCA and its use in dimension reduction for multivariate data.
• Comprehend more advanced methods such as MDS, MFA, t-SNE, UMAP, and their relevance to high-dimensional data analysis.
• Describe the concept of multi-omics factor analysis (MOFA) and its application to integrated multi-omics data.

2. Understand and Apply Supervised Dimension Reduction Methods

• Explain the principles of PCR and PLSR and how they differ from unsupervised techniques.

3. Develop practical skills in Dimension Reduction Methods

• Use hands-on exercises to confidently apply various dimension reduction techniques to real-world data using R.

Programming skills with R, e.g. course Introduction to R, basic knowledge of statistics, e.g. course Introduction to Statistics and knowledge on basic dimension reduction techniques (PCA), e.g. course Multivariate Statistics 1.