Statistical learning with high-dimensional data 7.5 credits

About the course

This course provides comprehensive knowledge, both regarding breadth and depth, about data science and statistical learning. In the course, both traditional and state of the art methods and algorithms in these fields are discussed. The related fundamental theories are also covered. After passing the course, the students should have a strong ability to solve problems through data. Meanwhile, students are also expected to have a strong self-study ability for understanding and learning any newly developed methods and algorithms.

Module 1 (3hp): Theory
Three families of approaches for dimensionality reduction are covered: spectral based learning (multi-dimensional Scaling, Isomap, Kernel PCA, etc.), manifold learning (Locally linear Embedding, Hessian Eigen-mapping, t-distributed stochastic neighbor embedding, etc.), and deep neural network-based methods (Autoencoders, Variational autoencoder, etc.). As special cases of dimensionality reduction, different feature selection methods, such as Ridge regression, LASSO, and Feature importance are also discussed. Supervised learning approaches including the Kernel-based methods (Kernel ridge regression, Support Vector Machine, etc.), Ensemble methods (Random Forest and Adaboost), Neural Networks, and different Deep Learning approaches and architectures are discussed. Furthermore unsupervised learning approaches including different clustering analysis algorithms, such as Density-based methods and Spectral clustering analysis are included. Deep learning-based unsupervised learning methods, such as Generative adversarial networks and its variations are also covered. Finally, fundamental mathematical theories about kernel methods, ensemble methods, penalty approaches, shallow network, gradient descent algorithm, universal estimator, and fundamental theorem of learning, etc. are discussed.

Module 2 (4.5hp): Computer labs
The module covers the analysis of several data sets, using the statistical methods that are included in the course. The analyses are conducted in one of the the programming languages R or Python. In the module, students write thorough reports of the analyses and the results from them.

Show syllabus

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Autumn 2025
- Statistical learning with high-dimensional data
  
  Autumn 2025 / Umeå / English / On site
  
  Submit a late application
  
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  Starts
  3 November 2025
  
  Ends
  18 January 2026
  
  Number of credits
  7.5 credits
  
  Type of studies
  On site
  
  Study pace
  50%
  
  Teaching hours
  Daytime
  
  Study location
  Umeå
  
  Language
  English
  
  Application code
  UMU-58211
  
  Eligibility The course requires 90 ECTS including 7,5 ECTS Computer Programming, 7,5 ECTS Multivariate Data Analysis and 12 ECTS Mathematical Statistics or equivalent. Proficiency in English and Swedish equivalent to the level required for basic eligibility for higher studies.
  
  Selection
  Guaranteed place
  
  Application
  Application deadline was 15 April 2025. Submit a late application at Universityadmissions.se.
  
  Application and tuition fees
  As a citizen of a country outside the European Union (EU), the European Economic Area (EEA) or Switzerland, you are required to pay application and tuition fees for studies at Umeå University.
  
  Application fee: SEK 900
  
  Tuition fee, first instalment: SEK 19,038
  
  Total fee: SEK 19,038
  
  Details about tuition, fees and funding

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