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.
Data Files
Click
here for the data directory.
(Last updated: 3rd December 2024 by John M. Noble)