John M. Noble
Mathematical Statistics
Institute of Applied Mathematics
University of Warsaw

October 2024 - January 2025

Multivariate Statistics

Course Information

Language: English
Type of course: elective

Place and Time

There are 14 lectures and 14 tutorials scheduled. These take place on Mondays. Lecture: 08.30 - 10.00 (room 5060) and tutorial 10.15 - 11.45 (room 2044: computer lab). Since Wednesday 2nd October 2024 and Thursday 9th January 2025 are ‘honorary Mondays’ (run according to the Monday schedule), the dates are:
October 2023 2nd (note: this is a Wednesday), 7th, 14th, 21st, 28th
November 2023 4th, 18th, 25th
December 2022 2nd, 9th, 16th
January 2023 9th (note: this is a Thursday), 13th, 20th

Description

The course ‘Multivariate Statistics’ is a Master's level course, giving some statistical theory, with application in R.

The topics covered are:

• Nonparametric Density Estimation (histograms, kernel methods, projection pursuit)
• Multiple regression: model assessment and selection, shrinkage methods (eg LASSO)
• Linear Dimensionality Reduction: Principal Component Analysis, Canonical Correlation Analysis, Projection Pursuit
• Linear Discriminant Analysis.
• Recursive Partitioning and Tree-based Methods
• Artificial Neural Networks
• Support Vector Machines
• Clustering techniques: hierarchical and non-hierarchical partitioning methods, self organising maps (SOM), clustering variables, clustering based on mixture models (the EM algorithm as a tool for clustering and semi-supervised learning).
• Multidimensional Scaling and Distance Geometry
• Committee Machines, Bagging and boosting, random forests
• Latent Variable Models for Blind Source Separation
• Nonlinear Dimensionality Reduction and Manifold Learning
• Correspondence Analysis
• The multivariate Gaussian distribution, parameter estimation, the Wishart distribution.

Introduction to R

You should learn some R programming throughout the course. A reasonable introduction may be found here.

Assessment

Assessment is based on

• two data analysis assignments
• a take home written exam
• Tutorial participation.

Lecture and Tutorial Notes

These will be placed here throughout the course.

• 2024-10-02: 08.30 - 10.00 Lecture 1: Nonparametric Density Estimation
• 2024-10-02: 10.15 - 11.45 Tutorial 1: Nonparametric Density Estimation
• 2024-10-02: 10.15 - 11.45 Tutorial 1: R script
• 2024-10-07: 08.30 - 10.00 Lecture 2: Biased Regression Methods
• 2024-10-07: 10.15 - 11.45 Tutorial 2: Biased Regression Methods
• 2024-10-07: 10.15 - 11.45 Tutorial 2: R script
• 2024-10-14: 08.30 - 10.00 Lecture 3: Penalised Regression
• 2024-10-14: 10.15 - 11.45 Tutorial 3: Biased Regression Methods
• 2024-10-14: 10.15 - 11.45 Tutorial 3: R script
• 2024-10-21: 08.30 - 10.00 Lecture 4: Canonical Correlation
• 2024-10-21: 10.15 - 11.45 Tutorial 4: Canonical Correlation
• 2024-10-21: 10.15 - 11.45 Tutorial 4: R script
• 2024-10-28: 08.30 - 10.00 Lecture 5: Linear Discriminant Function Analysis
• 2024-10-28: 10.15 - 11.45 Tutorial 5: Linear Discriminant Function Analysis
• 2024-10-28: 10.15 - 11.45 Tutorial 5: R script
• 2024-11-04: 08.30 - 10.00 Lecture 6: Classification and Regression Trees (CART)
• 2024-11-04: 10.15 - 11.45 Tutorial 6: Classification and Regression Trees (CART)
• 2024-11-04: 10.15 - 11.45 Tutorial 6: R script
• 2024-11-18: 08.30 - 10.00 Lecture 7: Support Vector Machines
• 2024-11-18: 10.15 - 11.45 Tutorial 7: Support Vector Machines
• 2024-11-18: 10.15 - 11.45 Tutorial 7: R script
• DATA ASSIGNMENT 1: DEADLINE - 2nd DECEMBER 2024, 13:00
• OBS! NO CLASSES ON 2024-11-25 (LECTURE AND TUTORIAL CANCELLED)
• 2024-12-02: 08.30 - 10.00 Lecture 8: Cluster Analysis
• 2024-12-02: 10.15 - 11.45 Tutorial 8: Cluster Analysis
• 2024-12-02: 10.15 - 11.45 Tutorial 8: R script
• 2024-12-09: 08.30 - 10.00 Lecture 9: Multidimensional Scaling
• 2024-12-09: 10.15 - 11.45 Tutorial 9: Multidimensional Scaling
• 2024-12-09: 10.15 - 11.45 Tutorial 9: R script
• 2024-12-16: 08.30 - 10.00 Lecture 10: Bagging, Boosting and Random Forests
• 2024-12-16: 10.15 - 11.45 Tutorial 10: Bagging, Boosting and Random Forests
• 2024-12-16: 10.15 - 11.45 Tutorial 10: R script
• 2025-01-09: 08.30 - 10.00 Lecture 11: Generalised Linear Models I
• 2025-01-09: 10.15 - 11.45 Tutorial 11: Generalised Linear Models I
• 2025-01-09: 10.15 - 11.45 Tutorial 11: R script

Data Files

Click here for the data directory.

(Last updated: 17th December 2024 by John M. Noble)